Academic literature on the topic 'Galerkin methods'

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Journal articles on the topic "Galerkin methods"

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Adjerid, Slimane, and Mahboub Baccouch. "Galerkin methods." Scholarpedia 5, no. 10 (2010): 10056. http://dx.doi.org/10.4249/scholarpedia.10056.

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Cross, M. "Computational Galerkin methods." Applied Mathematical Modelling 9, no. 3 (June 1985): 226. http://dx.doi.org/10.1016/0307-904x(85)90012-5.

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Marion, Martine, and Roger Temam. "Nonlinear Galerkin Methods." SIAM Journal on Numerical Analysis 26, no. 5 (October 1989): 1139–57. http://dx.doi.org/10.1137/0726063.

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Nakazawa, Shohei. "Computational Galerkin methods." Computer Methods in Applied Mechanics and Engineering 50, no. 2 (August 1985): 199–200. http://dx.doi.org/10.1016/0045-7825(85)90091-x.

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Cockburn, B. "Discontinuous Galerkin methods." ZAMM 83, no. 11 (November 3, 2003): 731–54. http://dx.doi.org/10.1002/zamm.200310088.

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Warburton, T. C., I. Lomtev, Y. Du, S. J. Sherwin, and G. E. Karniadakis. "Galerkin and discontinuous Galerkin spectral/hp methods." Computer Methods in Applied Mechanics and Engineering 175, no. 3-4 (July 1999): 343–59. http://dx.doi.org/10.1016/s0045-7825(98)00360-0.

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Banks, J. W., and T. Hagstrom. "On Galerkin difference methods." Journal of Computational Physics 313 (May 2016): 310–27. http://dx.doi.org/10.1016/j.jcp.2016.02.042.

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Canuto, C., R. H. Nochetto, and M. Verani. "Adaptive Fourier-Galerkin methods." Mathematics of Computation 83, no. 288 (November 21, 2013): 1645–87. http://dx.doi.org/10.1090/s0025-5718-2013-02781-0.

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Di Pietro, Daniele A. "Cell centered Galerkin methods." Comptes Rendus Mathematique 348, no. 1-2 (January 2010): 31–34. http://dx.doi.org/10.1016/j.crma.2009.11.012.

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Belytschko, T., Y. Y. Lu, and L. Gu. "Element-free Galerkin methods." International Journal for Numerical Methods in Engineering 37, no. 2 (January 30, 1994): 229–56. http://dx.doi.org/10.1002/nme.1620370205.

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Dissertations / Theses on the topic "Galerkin methods"

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Elfverson, Daniel. "On discontinuous Galerkin multiscale methods." Licentiate thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-200260.

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In this thesis a new multiscale method, the discontinuous Galerkin multiscale method, is proposed. The method uses localized fine scale computations to correct a global coarse scale equation and thereby takes the fine scale features into account. We show a priori error bounds for convection dominated diffusion-convection-reaction problems with variable coefficients. We also present a posteriori error bound in the case of no convection or reaction and present an adaptive algorithm which tunes the method parameters automatically. We also present extensive numerical experiments which verify our analytical findings.
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Dogan, Abdulkadir. "Petrov-Galerkin finite element methods." Thesis, Bangor University, 1997. https://research.bangor.ac.uk/portal/en/theses/petrovgalerkin-finite-element-methods(4d767fc7-4ad1-402a-9e6e-fd440b722406).html.

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Harbrecht, Helmut, and Reinhold Schneider. "Adaptive Wavelet Galerkin BEM." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600559.

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The wavelet Galerkin scheme for the fast solution of boundary integral equations produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that stays proportional to the number of unknowns. In this paper we present an adaptive version of the scheme which preserves the super-convergence of the Galerkin method.
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Casoni, Rero Eva. "Shock capturing for discontinuous Galerkin methods." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/51571.

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Aquesta tesi doctoral proposa formulacions de Galerkin Discontinu (DG) d’alt ordre per la captura de shocks, obtenint alhora solucions altament precises per problemes de flux compressible. En les últimes dècades, la investigació en els mètodes de DG ha estat en constant creixement. L'èxit dels mètodes DG en problemes hiperbòlics ha conduit el seu desenvolupament en lleis de conservació no lineals i problemes de convecció dominant. Entre els avantatges dels mètodes DG, destaquen la seva estabilitat inherent i les propietats locals de conservació. D'altra banda, els mètodes DG estan especialment dissenyats per l’ús aproximacions d'ordre superior. De fet, en els últims anys s'ha demostrat que la resolució de problemes de convecció dominant ja no es restringeix només a elements d'ordre inferior. De fet, es necessiten models numèrics d'alta precisió per aconseguir prediccions altament fiables dins la dinàmica de fluids computacional (CFD). En aquest context es presenten i discuteixen dos tècniques de captura de shocks. En primer lloc, es presenta una tècnica novedosa i senzilla basada en la introducció d'una nova base de funcions de forma. Aquesta base té la capacitat de canviar a nivell local entre una interpolació contínua o discontínua, depenent de la suavitat de la funció que es vol aproximar. En presència de xocs, les discontinuïtats introduïdes dins l’element permeten incloure l'estabilització necessària gràcies a l’ús dels fluxos numèrics, i alhora exploten les propietats intrínsiques del mètodes DG. En conseqüència, es poden utilitzar malles grolleres amb elements d’ordre superior. Amb aquestes discretitzacions i, utilitzant el mètode proposats, els xocs queden continguts a l’interior de l’element i per tant, és possible evitar l’ús de tècniques de refinament adaptatiu de la malla, alhora que es manté la localitat i compacitat dels esquemes DG. En segon lloc, es proposa una tècnica clàssica i, aparentment simple: la introducció de la viscositat artificial. Primerament es realitza un estudi detallat per al cas unidimensional. S’obté una viscositat d’alta precisió que escala segons el valor hk amb 1 ≤ k ≤ p i essent h la mida de l’element. En conseqüència, s’obté un xoc amb amplitud del mateix ordre. Seguidament, l'estudi de la viscositat unidimensional obtenida s'extén al cas multidimensional per a malles triangulars. L'extensió es basa en la projecció de la viscositat unidimensional en unes determinades direccions espacials dins l’element. Es demostra de manera consistent que la viscositat introduïda és, com a molt, del mateix ordre que la resolució donada per la discretització espacial, és a dir, h/p. El mètode és especialment eficient per aproximacions de Galerkin discontinu d’alt ordre, per exemple p≥ 3. Les dues metodologies es validen mitjançant una àmplia selecció d’exemples numèrics. En alguns exemples, els mètodes proposats permeten una reducció en el nombre de graus de llibertat necessaris per capturar xocs acuradament de fins i tot un ordre de magnitud, en comparació amb mètodes estàndar de refinament adaptatiu amb aproximacions de baix ordre.
This thesis proposes shock-capturing methods for high-order Discontinuous Galerkin (DG) formulations providing highly accurate solutions for compressible flows. In the last decades, research in DG methods has been very active. The success of DG in hyperbolic problems has driven many studies for nonlinear conservation laws and convection-dominated problems. Among all the advantages of DG, their inherent stability and local conservation properties are relevant. Moreover, DG methods are naturally suited for high-order approximations. Actually, in recent years it has been shown that convection-dominated problems are no longer restricted to low-order elements. In fact, highly accurate numerical models for High-Fidelity predictions in CFD are necessary. Under this rationale, two shock-capturing techniques are presented and discussed. First, a novel and simple technique based on on the introduction of a new basis of shape functions is presented. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization thanks to the numerical fluxes, thus exploiting DG inherent properties. Large high-order elements can therefore be used and shocks are captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Second, a classical and, apparently simple, technique is advocated: the introduction of artificial viscosity. First, a one-dimensional study is perfomed. Viscosity of the order O(hk) with 1≤ k≤ p is obtained, hence inducing a shock width of the same order. Second, the study extends the accurate one-dimensional viscosity to triangular multidimensional meshes. The extension is based on the projection of the one-dimensional viscosity into some characteristic spatial directions within the elements. It is consistently shown that the introduced viscosity scales, at most, withthe DG resolutions length scales, h/p. The method is especially reliable for highorder DG approximations, say p≥3. A wide range of different numerical tests validate both methodologies. In some examples the proposed methods allow to reduce by an order of magnitude the number of degrees of freedom necessary to accurately capture the shocks, compared to standard low order h-adaptive approaches.
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Murdoch, Thomas. "Galerkin methods for nonlinear elliptic equations." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329932.

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Dong, Zhaonan. "Discontinuous Galerkin methods on polytopic meshes." Thesis, University of Leicester, 2017. http://hdl.handle.net/2381/39140.

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This thesis is concerned with the analysis and implementation of the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) on computational meshes consisting of general polygonal/polyhedral (polytopic) elements. Two model problems are considered: general advection-diffusion-reaction boundary value problems and time dependent parabolic problems. New hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration as well as an arbitrary number of faces and hanging nodes per element. The proposed method employs elemental polynomial bases of total degree p (Pp- bases) defined in the physical coordinate system, without requiring mapping from a given reference or canonical frame. A series of numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a Pp-basis on both polytopic and tensor-product elements with a (standard) DGFEM and FEM employing a (mapped) Qp-basis. Moreover, a careful theoretical analysis of optimal convergence rate in p for Pp-basis is derived for several commonly used projectors, which leads to sharp bounds of exponential convergence with respect to degrees of freedom (dof) for the Pp-basis.
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Kovacs, Denis Christoph. "Inertial Manifolds and Nonlinear Galerkin Methods." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/30792.

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Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about the forcing term that is neglected by standard Galerkin. Moreover, we construct a simple postprocessing scheme that uses only this neglected information but gives the same increase in accuracy as nonlinear or postprocessed Galerkin methods.
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Harbrecht, Helmut, Ulf Kähler, and Reinhold Schneider. "Wavelet Galerkin BEM on unstructured meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601459.

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The present paper is devoted to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme. On the given mesh we construct a wavelet basis providing vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates can be compressed to $\mathcal{O}(N\log N)$ relevant matrix coefficients, where $N$ denotes the number of unknowns. The compressed system matrix can be computed within suboptimal complexity by using techniques from the fast multipole method or panel clustering. Numerical results prove that we succeeded in developing a fast wavelet Galerkin scheme for solving the considered class of problems.
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Of, Günther, Gregory J. Rodin, Olaf Steinbach, and Matthias Taus. "Coupling Methods for Interior Penalty Discontinuous Galerkin Finite Element Methods and Boundary Element Methods." Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-96885.

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This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.
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Galbraith, Marshall C. "A Discontinuous Galerkin Chimera Overset Solver." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1384427339.

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Books on the topic "Galerkin methods"

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Cockburn, Bernardo, George E. Karniadakis, and Chi-Wang Shu, eds. Discontinuous Galerkin Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-59721-3.

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Hesthaven, Jan S., and Tim Warburton. Nodal Discontinuous Galerkin Methods. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-72067-8.

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Smith, Ralph C. Sinc-Galerkin estimation of diffusivity in parabolic problems. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1991.

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L, Bowers Kenneth, and Langley Research Center, eds. Sinc-Galerkin estimation of diffusivity in parabolic problems. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1991.

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L, Bowers Kenneth, and Langley Research Center, eds. Sinc-Galerkin estimation of diffusivity in parabolic problems. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1991.

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Sutradhar, Alok. Symmetric galerkin boundary element method. Berlin: Springer, 2008.

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Rüter, Marcus Olavi. Error Estimates for Advanced Galerkin Methods. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06173-9.

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Wahlbin, Lars B. Superconvergence in Galerkin Finite Element Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0096835.

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Di Pietro, Daniele Antonio, and Alexandre Ern. Mathematical Aspects of Discontinuous Galerkin Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-22980-0.

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Wahlbin, Lars B. Superconvergence in Galerkin finite element methods. New York: Springer-Verlag, 1995.

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Book chapters on the topic "Galerkin methods"

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Le Maître, O. P., and O. M. Knio. "Galerkin Methods." In Scientific Computation, 73–105. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-3520-2_4.

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Wieners, Christian. "Galerkin Methods." In Encyclopedia of Applied and Computational Mathematics, 579–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_415.

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Rüter, Marcus Olavi. "Galerkin Methods." In Error Estimates for Advanced Galerkin Methods, 75–148. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06173-9_4.

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Uzunca, Murat. "Discontinuous Galerkin Methods." In Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows, 9–25. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30130-3_2.

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Larson, Mats G., and Fredrik Bengzon. "Discontinuous Galerkin Methods." In Texts in Computational Science and Engineering, 355–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33287-6_14.

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Girault, Vivette, and Mary F. Wheeler. "Discontinuous Galerkin Methods." In Partial Differential Equations, 3–26. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8758-5_1.

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Sullivan, T. J. "Stochastic Galerkin Methods." In Texts in Applied Mathematics, 251–76. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23395-6_12.

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Mehra, Mani. "Wavelet-Galerkin Methods." In Forum for Interdisciplinary Mathematics, 121–33. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2595-3_7.

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Kythe, Prem K., and Pratap Puri. "Sinc-Galerkin Methods." In Computational Methods for Linear Integral Equations, 286–320. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0101-4_10.

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Droniou, Jérôme, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin. "Discontinuous Galerkin Methods." In Mathématiques et Applications, 325–41. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-79042-8_11.

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Conference papers on the topic "Galerkin methods"

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Ko, Jeonghwan, Andrew Kurdila, and Michael Pilant. "Wavelet Galerkin multigrid methods." In 35th Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1994. http://dx.doi.org/10.2514/6.1994-1334.

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Cockburn, Bernardo. "The Hybridizable Discontinuous Galerkin Methods." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0166.

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Busch, Kurt. "Discontinuous Galerkin Methods in Nanophotonics." In Integrated Photonics Research, Silicon and Nanophotonics. Washington, D.C.: OSA, 2012. http://dx.doi.org/10.1364/iprsn.2012.im3b.1.

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Busch, Kurt, Michael Konig, Richard Diehl, Kirankumar R. Hiremath, and Jens Niegemann. "Discontinuous Galerkin methods for nano-photonics." In 2011 ICO International Conference on Information Photonics (IP). IEEE, 2011. http://dx.doi.org/10.1109/ico-ip.2011.5953772.

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Kessler, Manuel. "Engineering Application Oriented Discontinuous Galerkin Methods." In 45th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-511.

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Busch, Kurt. "Discontinuous Galerkin methods in nano-photonics." In 2016 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD). IEEE, 2016. http://dx.doi.org/10.1109/nusod.2016.7547102.

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Dazel, Olivier, and Gwenael Gabard. "Discontinuous Galerkin Methods for poroelastic materials." In ICA 2013 Montreal. ASA, 2013. http://dx.doi.org/10.1121/1.4799714.

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Collis, S. Scott, and Kaveh Ghayour. "Discontinuous Galerkin Methods for Compressible DNS." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45632.

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A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to a range of test problems including steady and unsteady flow over a circular cylinder, inviscid flow over an inclined ellipse, and fully developed turbulent flow in a planar channel. In all cases, local hp-refinement is utilized to obtain high quality solutions with fewer degrees of freedom than traditional numerical methods. The formulation and validation cases presented here lay the foundation for future applications of DG for simulation of compressible turbulent flows in complex geometries.
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Huynh, H. T. "Collocation and Galerkin Time-Stepping Methods." In 19th AIAA Computational Fluid Dynamics. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-4323.

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Mata Almonacid, Pablo, Yongxing Shen, and Vahid Ziaei-Rad. "A VARIATIONAL FORMULATION OF DISCONTINUOUS-GALERKIN TIME INTEGRATORS." In 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering Methods in Structural Dynamics and Earthquake Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2015. http://dx.doi.org/10.7712/120115.3458.1050.

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Reports on the topic "Galerkin methods"

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Belytschko, Ted. Crack Propagation by Element-Free Galerkin Methods. Fort Belvoir, VA: Defense Technical Information Center, May 1997. http://dx.doi.org/10.21236/ada329723.

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Garikipati, Krishna, and Jakob T. Ostien. Discontinuous Galerkin finite element methods for gradient plasticity. Office of Scientific and Technical Information (OSTI), October 2010. http://dx.doi.org/10.2172/1008112.

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Watkins, Jerry. Current Status of Discontinuous Galerkin (DG) methods in SPARC. Office of Scientific and Technical Information (OSTI), September 2019. http://dx.doi.org/10.2172/1564038.

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Cyr, Eric C. Spatially varying embedded stochastic galerkin methods for steady-state PDEs. Office of Scientific and Technical Information (OSTI), July 2013. http://dx.doi.org/10.2172/1090207.

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Heineike, Benjamin M. Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods. Fort Belvoir, VA: Defense Technical Information Center, May 2002. http://dx.doi.org/10.21236/ada403766.

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Xia, Yinhua, Yan Xu, and Chi-Wang Shu. Local Discontinuous Galerkin Methods for the Cahn-Hilliard Type Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2007. http://dx.doi.org/10.21236/ada464873.

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Giraldo, F. X., J. S. Hesthaven, and T. Warburton. Nodal High-Order Discontinuous Galerkin Methods for the Spherical Shallow Water Equations. Fort Belvoir, VA: Defense Technical Information Center, September 2002. http://dx.doi.org/10.21236/ada633613.

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Giraldo, F. X., J. S. Hesthaven, and T. Warburton. Nodal High-Order Discontinuos Galerkin Methods for the Spherical Shallow Water Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada461874.

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Roberts, Nathaniel David, Pavel Blagoveston Bochev, Leszek D. Demkowicz, and Denis Ridzal. A toolbox for a class of discontinuous Petrov-Galerkin methods using trilinos. Office of Scientific and Technical Information (OSTI), September 2011. http://dx.doi.org/10.2172/1029782.

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Mezzacappa, Anthony, Eirik Endeve, Cory D. Hauck, and Yulong Xing. Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates. Office of Scientific and Technical Information (OSTI), February 2015. http://dx.doi.org/10.2172/1394128.

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