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Relevant bibliographies by topics / Dirichlet boundary condition

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Academic literature on the topic 'Dirichlet boundary condition'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Dirichlet boundary condition"

1

Cao, Shunhua, and Stewart Greenhalgh. "Attenuating boundary conditions for numerical modeling of acoustic wave propagation." GEOPHYSICS 63, no. 1 (1998): 231–43. http://dx.doi.org/10.1190/1.1444317.

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Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one‐wavelength wide zone. The Neumann‐attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmittin

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Park, I. Y. "Quantum “violation” of Dirichlet boundary condition." Physics Letters B 765 (February 2017): 260–64. http://dx.doi.org/10.1016/j.physletb.2016.12.026.

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Diyab, Farah, and B. Surender Reddy. "Comparison of Laplace Beltrami Operator Eigenvalues on Riemannian Manifolds." European Journal of Mathematics and Statistics 3, no. 5 (2022): 55–60. http://dx.doi.org/10.24018/ejmath.2022.3.5.143.

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Let $\Delta_{g}$ be the Laplace Beltrami operator on a manifold $M$ with Dirichlet (resp.,Neumann) boundary conditions. We compare the spectrum of on a Riemannian manifold for Neumann boundary condition and Dirichlet boundary condition . Then we construct aneffective method of obtaining small eigenvalues for Neumann's problem.

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Turmetov, B. Kh, and V. V. Karachik. "NEUMANN BOUNDARY CONDITION FOR A NONLOCAL BIHARMONIC EQUATION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 2 (2022): 51–58. http://dx.doi.org/10.14529/mmph220205.

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The solvability conditions for a class of boundary value problems for a nonlocal biharmonic equation in the unit ball with the Neumann conditions on the boundary are studied. The nonlocality of the equation is generated by some orthogonal matrix. The presence and uniqueness of a solution to the proposed Neumann boundary condition is examined, and an integral representation of the solution to the Dirichlet problem in terms of the Green's function for the biharmonic equation in the unit ball is obtained. First, some auxiliary statements are established: the Green's function of the Dirichlet prob

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Corrêa, Francisco Julio S. A., and Joelma Morbach. "A Dirichlet problem under integral boundary condition." Journal of Mathematical Analysis and Applications 478, no. 1 (2019): 1–13. http://dx.doi.org/10.1016/j.jmaa.2019.04.030.

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Amrouche, Cherif, and Šárka Nečasová. "Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition." Mathematica Bohemica 126, no. 2 (2001): 265–74. http://dx.doi.org/10.21136/mb.2001.134013.

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Yosaf, Asma, Shafiq Ur Rehman, Fayyaz Ahmad, Malik Zaka Ullah, and Ali Saleh Alshomrani. "Eighth-Order Compact Finite Difference Scheme for 1D Heat Conduction Equation." Advances in Numerical Analysis 2016 (May 16, 2016): 1–12. http://dx.doi.org/10.1155/2016/8376061.

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The purpose of this paper is to develop a high-order compact finite difference method for solving one-dimensional (1D) heat conduction equation with Dirichlet and Neumann boundary conditions, respectively. A parameter is used for the direct implementation of Dirichlet and Neumann boundary conditions. The introduced parameter adjusts the position of the neighboring nodes very next to the boundary. In the case of Dirichlet boundary condition, we developed eighth-order compact finite difference method for the entire domain and fourth-order accurate proposal is presented for the Neumann boundary c

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Hayasida, Kazuya, and Masao Nakatani. "On the Dirichlet problem of prescribed mean curvature equations without H-convexity condition." Nagoya Mathematical Journal 157 (2000): 177–209. http://dx.doi.org/10.1017/s0027763000007248.

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The Dirichlet problem of prescribed mean curvature equations is well posed, if the boundery is H-convex. In this article we eliminate the H-convexity condition from a portion Γ of the boundary and prove the existence theorem, where the boundary condition is satisfied on Γ in the weak sense.

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Algazin, O. D., and A. V. Kopaev. "A Mixed Boundary Value Problem for the Laplace Equation in a semi-infinite Layer." Mathematics and Mathematical Modeling, no. 5 (February 6, 2021): 1–12. http://dx.doi.org/10.24108/mathm.0520.0000229.

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The paper offers a solution of the mixed Dirichlet-Neumann and Dirichlet-Neumann-Robin boundary value problems for the Laplace equation in the semi-infinite layer, using the previously obtained solution of the mixed Dirichlet-Neumann boundary value problem for a layer.The functions on the right-hand sides of the boundary conditions are considered to be functions of slow growth, in particular, polynomials. The solution to boundary value problems is also sought in the class of functions of slow growth. Continuing the functions on the right-hand sides of the boundary conditions on the upper and l

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YAKUBOV, YAKOV. "COMPLETENESS OF ROOT FUNCTIONS AND ELEMENTARY SOLUTIONS OF THE THERMOELASTICITY SYSTEM." Mathematical Models and Methods in Applied Sciences 05, no. 05 (1995): 587–98. http://dx.doi.org/10.1142/s0218202595000346.

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In this paper we prove the completeness of the root functions (eigenfunctions and associated functions) of an elliptic system (in the sense of Douglis-Nirenberg) corresponding to the thermoelasticity system with the Dirichlet boundary value condition. The problem is considered in a domain with a non-smooth boundary. Then an initial boundary value problem corresponding to the thermoelasticity system with the Dirichlet boundary value condition is considered. We find sufficient conditions that guarantee an approximation of a solution to the initial boundary value problem by linear combinations of

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Dissertations / Theses on the topic "Dirichlet boundary condition"

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Yang, Xue. "Neumann problems for second order elliptic operators with singular coefficients." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html.

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In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients, and reveal the relationship between the solution to the partial differential equation (PDE in abbreviation) and the solution to a kind of backward stochastic differential equations (BSDE in abbreviation).This study is motivated by the research on the Dirichlet problem for an elliptic operator (\cite{Z}). But it turns out that different methods are needed to deal with the reflecting diffusion on a bounded domain. For example, the i

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Cheaytou, Rima. "Etude des méthodes de pénalité-projection vectorielle pour les équations de Navier-Stokes avec conditions aux limites ouvertes." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4715.

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L'objectif de cette thèse consiste à étudier la méthode de pénalité-projection vectorielle notée VPP (Vector Penalty-Projection method), qui est une méthode à pas fractionnaire pour la résolution des équations de Navier-Stokes incompressible avec conditions aux limites ouvertes. Nous présentons une revue bibliographique des méthodes de projection traitant le couplage de vitesse et de pression. Nous nous intéressons dans un premier temps aux conditions de Dirichlet sur toute la frontière. Les tests numériques montrent une convergence d'ordre deux en temps pour la vitesse et la pression et prouv

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Choulli, Mourad. "Identifiabilite d'un parametre dans une equation parabolique non lineaire monodimensionnelle." Toulouse 3, 1987. http://www.theses.fr/1987TOU30245.

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Etude, essentiellement basee sur des techniques utilisant le principe du maximum pour les equations paraboliques lineaires, permettant de discuter du probleme d'identifiabilite du parametre qui apparait dans une equation de diffusion non lineaire

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Matsui, Kazunori. "Asymptotic analysis of an ε-Stokes problem with Dirichlet boundary conditions". Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-71938.

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In this thesis, we propose an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one pa- rameter ε > 0. We prove that the solution to the ε-Stokes problem, converges as ε tends to 0 or ∞ to the Stokes and pressure-Poisson prob- lem, respectively. Most of these results are new. The precise statements of the new results are given in Proposition 3.5, Theorem 4.1, Theorem 5.2, and Theorem 5.3. Numerical results illustrating our mathematical results are also presented.<br>STINT (DD2017-6936) "Mathematics Bachelor Program for Efficient Computation

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Couture, Chad. "Steady States and Stability of the Bistable Reaction-Diffusion Equation on Bounded Intervals." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37110.

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Reaction-diffusion equations have been used to study various phenomena across different fields. These equations can be posed on the whole real line, or on a subinterval, depending on the situation being studied. For finite intervals, we also impose diverse boundary conditions on the system. In the present thesis, we solely focus on the bistable reaction-diffusion equation while working on a bounded interval of the form $[0,L]$ ($L>0$). Furthermore, we consider both mixed and no-flux boundary conditions, where we extend the former to Dirichlet boundary conditions once our analysis of that syst

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PERROTTA, Antea. "Differential Formulation coupled to the Dirichlet-to-Neumann operator for scattering problems." Doctoral thesis, Università degli studi di Cassino, 2020. http://hdl.handle.net/11580/75845.

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This Thesis proposes the use of the Dirichlet-to-Neumann (DtN) operator to improve the accuracy and the efficiency of the numerical solution of an electromagnetic scattering problem, described in terms of a differential formulation. From a general perspective, the DtN operator provides the “connection” (the mapping) between the Dirichlet and the Neumann data onto a proper closed surface. This allows truncation of the computational domain when treating a scattering problem in an unbounded media. Moreover, the DtN operator provides an exact boundary condition, in contrast to other methods such a

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Marco, Alacid Onofre. "Structural Shape Optimization Based On The Use Of Cartesian Grids." Doctoral thesis, Universitat Politècnica de València, 2018. http://hdl.handle.net/10251/86195.

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As ever more challenging designs are required in present-day industries, the traditional trial-and-error procedure frequently used for designing mechanical parts slows down the design process and yields suboptimal designs, so that new approaches are needed to obtain a competitive advantage. With the ascent of the Finite Element Method (FEM) in the engineering community in the 1970s, structural shape optimization arose as a promising area of application. However, due to the iterative nature of shape optimization processes, the handling of large quantities of numerical models along with the ap

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Coco, Armando. "Finite-Difference Ghost-Cell Multigrid Methods for Elliptic problems with Mixed Boundary Conditions and Discontinuous Coefficients." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1107.

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The work of this thesis is devoted to the development of an original and general numerical method for solving the elliptic equation in an arbitrary domain (described by a level-set function) with general boundary conditions (Dirichlet, Neumann, Robin, ...) using Cartesian grids. It can be then considered an immersed boundary method, and the scheme we use is based on a finite-difference ghost-cell technique. The entire problem is solved by an effective multigrid solver, whose components have been suitably constructed in order to be applied to the scheme. The method is extended to the more chal

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Eschke, Andy. "Analytical solution of a linear, elliptic, inhomogeneous partial differential equation with inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions for a special rotationally symmetric problem of linear elasticity." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-149965.

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The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary condition

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Junior, Vanderley Alves Ferreira. "Problemas de valores de contorno envolvendo o operador biharmônico." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-20032013-083331/.

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Estudamos o problema de valores de contorno {\'DELTA POT. 2\' u = f em \'OMEGA\', \'BETA\' u = 0 em \'PARTIAL OMEGA\', um aberto limitado \'OMEGA\' \'ESTÁ CONTIDO\' \'R POT. N\' , sob diferentes condições de contorno. As questões de existência e positividade de soluções para este problema são abordadas com condições de contorno de Dirichlet, Navier e Steklov. Deduzimos condições de contorno naturais através do estudo de um modelo para uma placa com carga estática. Estudamos ainda propriedades do primeiro autovalor de \'DELTA POT. 2\' e o problema semilinear {\'DELTA POT. 2\' u = F (u) em \'OM

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Books on the topic "Dirichlet boundary condition"

1

J, Liandrat, and Institute for Computer Applications in Science and Engineering., eds. On the effective construction of compactly supported wavelets satisfying homogenous boundary conditions on the interval. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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2

Adi, Ditkowski, and Institute for Computer Applications in Science and Engineering., eds. Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Adi, Ditkowski, and Institute for Computer Applications in Science and Engineering., eds. Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Adi, Ditkowski, and Institute for Computer Applications in Science and Engineering., eds. Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Mann, Peter. The Stationary Action Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0007.

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This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed i

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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I: Dirichlet Boundary Conditions on Euclidean Space. Springer International Publishing AG, 2022.

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Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Bounded error schemes for the wave equation on complex domains. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators inclu

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Book chapters on the topic "Dirichlet boundary condition"

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Bianchi, Massimo, Roland Allen, Antonio Mondragon, et al. "Dirichlet-Neumann Boundary Condition." In Concise Encyclopedia of Supersymmetry. Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_162.

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Motreanu, Dumitru, and Zdzisław Naniewicz. "Semilinear Hemivariational Inequalities with Dirichlet Boundary Condition." In Advances in Mechanics and Mathematics. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-4435-4_2.

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Grote, Marcus J., and Christoph Kirsch. "Dirichlet-to-Neumann Boundary Condition for Multiple Scattering Problems." In Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55856-6_42.

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Piasecki, Tomasz, and Milan Pokorný. "Steady Compressible Navier–Stokes–Fourier System with Slip Boundary Condition for the Velocity and Dirichlet Boundary Condition for the Temperature." In Fluids Under Control. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27625-5_8.

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Pokorný, Milan. "Steady Compressible Navier–Stokes–Fourier Equations with Dirichlet Boundary Condition for the Temperature." In Collected Papers in Honor of Yoshihiro Shibata. Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-19252-4_14.

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Schmitz, Hermann. "A collocation method for potential problems with a mixed Dirichlet-Signorini boundary condition." In Teubner-Texte zur Mathematik. Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-11577-9_20.

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Ezhak, Svetlana. "On Estimates for the First Eigenvalue of the Sturm–Liouville Problem with Dirichlet Boundary Conditions and Integral Condition." In Differential and Difference Equations with Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_32.

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Droniou, Jérôme, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin. "Dirichlet Boundary Conditions." In Mathématiques et Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-79042-8_2.

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Feltrin, Guglielmo. "Dirichlet Boundary Conditions." In Positive Solutions to Indefinite Problems. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94238-4_1.

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Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Nonlinear Elliptic Equations with Dirichlet Boundary Conditions." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_11.

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Conference papers on the topic "Dirichlet boundary condition"

1

Qiaoling Jiang, Weige Wu, and Jianxin Liu. "Monte Carlo method for Dirichlet boundary condition of multimedia field." In 2009 International Conference on Microwave Technology and Computational Electromagnetics (ICMTCE 2009). IET, 2009. http://dx.doi.org/10.1049/cp.2009.1356.

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Ashyralyev, Allaberen, Kadriye Tuba Turkcan, and Mehmet Emir Koksal. "Numerical solutions of telegraph equations with the Dirichlet boundary condition." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959669.

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Yusop, Nur Syaza Mohd, and Nurul Akmal Mohamed. "The system of equations for mixed BVP with one Dirichlet boundary condition and three Neumann boundary conditions." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON EDUCATION, MATHEMATICS AND SCIENCE 2016 (ICEMS2016) IN CONJUNCTION WITH 4TH INTERNATIONAL POSTGRADUATE CONFERENCE ON SCIENCE AND MATHEMATICS 2016 (IPCSM2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4983857.

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Yao, Guangfa. "A Simple Immersed Boundary Method for Modeling Forced Convection Heat Transfer." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10236.

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Abstract As non-body conforming numerical methods using simple Cartesian mesh, immersed boundary methods have become increasingly popular in modeling fluid-solid interaction. They usually do this by adding a body force term in the momentum equation. The magnitude and direction of this body force ensure that the boundary condition on the solid-fluid interface is satisfied without invoking complicated body-conforming numerical methods to impose the boundary condition. A similar path has been followed to model forced convection heat transfer by adding a source term in the energy equation. The add

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Jablonski, Pawel. "Approaches to mixed Dirichlet-Neumann boundary condition in the method of separation of variables." In 2019 Applications of Electromagnetics in Modern Techniques and Medicine (PTZE). IEEE, 2019. http://dx.doi.org/10.23919/ptze.2019.8781727.

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Junhong, Liu, Liu Wenxue, Li Lifeng, and Jin Qi. "Oscillation criteria for a class of nonlinear impulsive parabolic system under Dirichlet boundary condition." In 2015 International Conference on Advanced Mechatronic Systems (ICAMechS). IEEE, 2015. http://dx.doi.org/10.1109/icamechs.2015.7287129.

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Danarwindu, Ghiffari Ahnaf, and Nikenasih Binatari. "Green's function for convection diffusion equation with Dirichlet boundary condition using separation variable's method." In PROCEEDINGS OF THE 4TH INTERNATIONAL SEMINAR ON INNOVATION IN MATHEMATICS AND MATHEMATICS EDUCATION (ISIMMED) 2020: Rethinking the role of statistics, mathematics and mathematics education in society 5.0: Theory, research, and practice. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108795.

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Surmont, Florian, and Damien Coache. "Investigation on the Shooting Method Ability to Solve Different Mooring Lines Boundary Condition Types." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-77563.

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The study of undersea cables and mooring lines statics remains an unavoidable subject of simulation in offshore field for either steady-state analysis or dynamic simulation initialization. Whether the study concerns mooring systems pinned both at seabed and floating platform, cables towed by a moving underwater system or when special links such as stiffeners are needed, the ability to model every combination is a key point. To do so the authors propose to investigate the use of the shooting method to solve the two point boundary value problem (TPBVP) associated with Dirichlet, Robin or mixed b

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Ahmad, Muhammad Jalil, and Korhan Günel. "Numerical Solution of Dirichlet Boundary Value Problems using Mesh Adaptive Direct Search Optimization." In International Students Science Congress. Izmir International Guest Student Association, 2021. http://dx.doi.org/10.52460/issc.2021.030.

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This study gives a different numerical approach for solving second order differential equation with a Dirichlet boundary condition. Mesh Adaptive Direct Search (MADS) algorithm is adopted to train the feed forward neural network used in this approach. As MADS is a derivative-free optimization algorithm, it helps us to reduce the time-consuming workload in the training stage. The results obtained from this approach are also compared with Generalized Pattern Search (GPS) algorithm.

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Atassi, Hafiz M., and Romeo F. Susan-Resiga. "Parallel Computation of Harmonic Waves Using Domain Decomposition: Part 1 — General Formulation." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0532.

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Abstract A method is presented for parallel computation of time-harmonic waves using an iterative scheme based on domain decomposition. For exterior radiation and scattering problems, a finite computational domain is obtained by introducing a computational outer boundary on which a modified Dirichlet-to-Neumann map is used as a nonreflecting condition. The computational domain is then decomposed into subdomains and for each a boundary-value problem is defined using impedance-like transmission conditions on the subdomain interfaces. An iterative scheme updates the subdomain boundary conditions

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Reports on the topic "Dirichlet boundary condition"

1

Babuska, Ivo, Victor Nistor, and Nicolae Tarfulea. Approximate Dirichlet Boundary Conditions in the Generalized Finite Element Method (PREPRINT). Defense Technical Information Center, 2006. http://dx.doi.org/10.21236/ada478502.

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Babuska, Ivo, B. Guo, and Manil Suri. Implementation of Nonhomogeneous Dirichlet Boundary Conditions in the p- Version of the Finite Element Method. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada207799.

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