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Artículos de revistas sobre el tema "High-Order finite element methods"

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Publicado: 8 de junio de 2024

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1

Abreu, Eduardo, Ciro Díaz, Juan Galvis y Marcus Sarkis. "On high-order conservative finite element methods". Computers & Mathematics with Applications 75, n.º 6 (marzo de 2018): 1852–67. http://dx.doi.org/10.1016/j.camwa.2017.10.020.

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2

Harari, Isaac y Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems". Journal of Computational Acoustics 05, n.º 01 (marzo de 1997): 33–51. http://dx.doi.org/10.1142/s0218396x97000046.

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The goal of this work is to design and analyze quadratic finite elements for problems of time-harmonic acoustics, and to compare the computational efficiency of quadratic elements to that of lower-order elements. Non-reflecting boundary conditions yield an equivalent problem in a bounded region which is suitable for domain-based computation of solutions to exterior problems. Galerkin/least-squares technology is utilized to develop robust methods in which stability properties are enhanced while maintaining higher-order accuracy. The design of Galerkin/least-squares methods depends on the order of interpolation employed, and in this case quadratic elements are designed to yield dispersion-free solutions to model problems. The accuracy of Galerkin/least-squares and traditional Galerkin elements is compared, as well as the accuracy of quadratic versus standard linear interpolation, incorporating the effects of representing the radiation condition in exterior problems. The efficiency of the various methods is measured in terms of the cost of computation, rather than resolution requirements. In this manner, clear guidelines for selecting the order of interpolation are derived. Numerical testing validates the superior performance of the proposed methods. This work is a first step to gaining a thorough analytical understanding of the performance of p refinement as a basis for the development of h-p finite element methods for large-scale computation of solutions to acoustic problems.

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3

Bagheri, Babak, L. Ridgway Scott y Shangyou Zhang. "Implementing and using high-order finite element methods". Finite Elements in Analysis and Design 16, n.º 3-4 (junio de 1994): 175–89. http://dx.doi.org/10.1016/0168-874x(94)90063-9.

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4

Lin, Qun y Junming Zhou. "Superconvergence in high-order Galerkin finite element methods". Computer Methods in Applied Mechanics and Engineering 196, n.º 37-40 (agosto de 2007): 3779–84. http://dx.doi.org/10.1016/j.cma.2006.10.027.

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5

Larson, Mats G. y Sara Zahedi. "Stabilization of high order cut finite element methods on surfaces". IMA Journal of Numerical Analysis 40, n.º 3 (25 de abril de 2019): 1702–45. http://dx.doi.org/10.1093/imanum/drz021.

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Abstract We develop and analyse a stabilization term for cut finite element approximations of an elliptic second-order partial differential equation on a surface embedded in ${\mathbb{R}}^d$. The new stabilization term combines properly scaled normal derivatives at the surface together with control of the jump in the normal derivatives across faces, and provides control of the variation of the finite element solution on the active three-dimensional elements that intersect the surface. We show that the condition number of the stiffness matrix is $O(h^{-2})$, where $h$ is the mesh parameter. The stabilization term works for linear as well as for higher-order elements and the derivation of its stabilizing properties is quite straightforward, which we illustrate by discussing the extension of the analysis to general $n$-dimensional smooth manifolds embedded in ${\mathbb{R}}^d$, with codimension $d-n$. We also state the properties of a general stabilization term that are sufficient to prove optimal scaling of the condition number and optimal error estimates in energy- and $L^2$-norm. We finally present numerical studies confirming our theoretical results.

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6

Winther, Kaibo Hu &. Ragnar. "Well-Conditioned Frames for High Order Finite Element Methods". Journal of Computational Mathematics 39, n.º 3 (junio de 2021): 333–57. http://dx.doi.org/10.4208/jcm.2001-m2018-0078.

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7

Dobrev, Veselin A., Tzanio V. Kolev y Robert N. Rieben. "High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics". SIAM Journal on Scientific Computing 34, n.º 5 (enero de 2012): B606—B641. http://dx.doi.org/10.1137/120864672.

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8

Yurun, Fan y M. J. Crochet. "High-order finite element methods for steady viscoelastic flows". Journal of Non-Newtonian Fluid Mechanics 57, n.º 2-3 (mayo de 1995): 283–311. http://dx.doi.org/10.1016/0377-0257(94)01338-i.

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9

Opschoor, Joost A. A., Philipp C. Petersen y Christoph Schwab. "Deep ReLU networks and high-order finite element methods". Analysis and Applications 18, n.º 05 (21 de febrero de 2020): 715–70. http://dx.doi.org/10.1142/s0219530519410136.

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Approximation rate bounds for emulations of real-valued functions on intervals by deep neural networks (DNNs) are established. The approximation results are given for DNNs based on ReLU activation functions. The approximation error is measured with respect to Sobolev norms. It is shown that ReLU DNNs allow for essentially the same approximation rates as nonlinear, variable-order, free-knot (or so-called “[Formula: see text]-adaptive”) spline approximations and spectral approximations, for a wide range of Sobolev and Besov spaces. In particular, exponential convergence rates in terms of the DNN size for univariate, piecewise Gevrey functions with point singularities are established. Combined with recent results on ReLU DNN approximation of rational, oscillatory, and high-dimensional functions, this corroborates that continuous, piecewise affine ReLU DNNs afford algebraic and exponential convergence rate bounds which are comparable to “best in class” schemes for several important function classes of high and infinite smoothness. Using composition of DNNs, we also prove that radial-like functions obtained as compositions of the above with the Euclidean norm and, possibly, anisotropic affine changes of co-ordinates can be emulated at exponential rate in terms of the DNN size and depth without the curse of dimensionality.

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10

Jund, Sébastien y Stéphanie Salmon. "Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping". International Journal of Applied Mathematics and Computer Science 17, n.º 3 (1 de octubre de 2007): 375–93. http://dx.doi.org/10.2478/v10006-007-0031-2.

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Arbitrary High-Order Finite Element Schemes and High-Order Mass LumpingComputers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of orderkand show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up toP5elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.

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11

Akrivis, Georgios. "High-order finite element methods for the Kuramoto-Sivashinsky equation". ESAIM: Mathematical Modelling and Numerical Analysis 30, n.º 2 (1996): 157–83. http://dx.doi.org/10.1051/m2an/1996300201571.

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12

Vidal-Ferràndiz, A., S. González-Pintor, D. Ginestar, G. Verdú, M. Asadzadeh y C. Demazière. "Use of discontinuity factors in high-order finite element methods". Annals of Nuclear Energy 87 (enero de 2016): 728–38. http://dx.doi.org/10.1016/j.anucene.2015.06.021.

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13

Xiao, Yuanming, Jinchao Xu y Fei Wang. "High-order extended finite element methods for solving interface problems". Computer Methods in Applied Mechanics and Engineering 364 (junio de 2020): 112964. http://dx.doi.org/10.1016/j.cma.2020.112964.

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14

Rank, Ernst, Zohar Yosibash y Alexander Düster. "HOFEM07 – International workshop on high-order finite element methods, 2007". Computer Methods in Applied Mechanics and Engineering 198, n.º 13-14 (marzo de 2009): 1125. http://dx.doi.org/10.1016/j.cma.2009.01.002.

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15

MIURA, Shinichiro. "214 Turbulent channel flow Analysis of Finite Element Methods with High-Order Element". Proceedings of Conference of Kansai Branch 2006.81 (2006): _2–20_. http://dx.doi.org/10.1299/jsmekansai.2006.81._2-20_.

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16

Lu, Qiukai, Mark S. Shephard, Saurabh Tendulkar y Mark W. Beall. "Parallel mesh adaptation for high-order finite element methods with curved element geometry". Engineering with Computers 30, n.º 2 (20 de septiembre de 2013): 271–86. http://dx.doi.org/10.1007/s00366-013-0329-7.

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17

Cui, Ming, Yanxin Su y Dong Liang. "High-Order Finite Volume Methods for Aerosol Dynamic Equations". Advances in Applied Mathematics and Mechanics 8, n.º 2 (27 de enero de 2016): 213–35. http://dx.doi.org/10.4208/aamm.2013.m362.

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AbstractAerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. In this paper we consider numerical methods for the nonlinear aerosol dynamic equations on time and particle size. The finite volume element methods based on the linear interpolation and Hermite interpolation are provided to approximate the aerosol dynamic equation where the condensation and removal processes are considered. Numerical examples are provided to show the efficiency of these numerical methods.

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18

Świrydowicz, Kasia, Noel Chalmers, Ali Karakus y Tim Warburton. "Acceleration of tensor-product operations for high-order finite element methods". International Journal of High Performance Computing Applications 33, n.º 4 (9 de enero de 2019): 735–57. http://dx.doi.org/10.1177/1094342018816368.

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19

Jiang, Yingjun y Jingtang Ma. "High-order finite element methods for time-fractional partial differential equations". Journal of Computational and Applied Mathematics 235, n.º 11 (abril de 2011): 3285–90. http://dx.doi.org/10.1016/j.cam.2011.01.011.

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20

Wildey, Tim, Sriramkrishnan Muralikrishnan y Tan Bui-Thanh. "Unified Geometric Multigrid Algorithm for Hybridized High-Order Finite Element Methods". SIAM Journal on Scientific Computing 41, n.º 5 (enero de 2019): S172—S195. http://dx.doi.org/10.1137/18m1193505.

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21

Li, Long-yuan y Peter Bettess. "Adaptive Finite Element Methods: A Review". Applied Mechanics Reviews 50, n.º 10 (1 de octubre de 1997): 581–91. http://dx.doi.org/10.1115/1.3101670.

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The adaptive finite element method (FEM) was developed in the early 1980s. The basic concept of adaptivity developed in the FEM is that, when a physical problem is analyzed using finite elements, there exist some discretization errors caused owing to the use of the finite element model. These errors are calculated in order to assess the accuracy of the solution obtained. If the errors are large, then the finite element model is refined through reducing the size of elements or increasing the order of interpolation functions. The new model is re-analyzed and the errors in the new model are recalculated. This procedure is continued until the calculated errors fall below the specified permissible values. The key features in the adaptive FEM are the estimation of discretization errors and the refinement of finite element models. This paper presents a brief review of the methods for error estimates and adaptive refinement processes applied to finite element calculations. The basic theories and principles of estimating finite element discretization errors and refining finite element models are presented. This review article contains 131 references.

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22

Bradji, Abdallah y Jürgen Fuhrmann. "Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method". Mathematica Bohemica 139, n.º 2 (2014): 125–36. http://dx.doi.org/10.21136/mb.2014.143843.

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23

Yi, Tae-Hyeong y Francis X. Giraldo. "Vertical Discretization for a Nonhydrostatic Atmospheric Model Based on High-Order Spectral Elements". Monthly Weather Review 148, n.º 1 (27 de diciembre de 2019): 415–36. http://dx.doi.org/10.1175/mwr-d-18-0283.1.

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Abstract This study addresses the treatment of vertical discretization for a high-order, spectral element model of a nonhydrostatic atmosphere in which the governing equations of the model are separated into horizontal and vertical components by introducing a coordinate transformation, so that one can use different orders and types of approximations in both directions. The vertical terms of the decoupled governing equations are discretized using finite elements based on either Lagrange or basis-spline polynomial functions in the sigma coordinate, while maintaining the high-order spectral elements for the discretization of the horizontal terms. This leads to the fact that the high-order model of spectral elements with a nonuniform grid, interpolated within an element, can be easily accommodated with existing physical parameterizations. Idealized tests are performed to compare the accuracy and efficiency of the vertical discretization methods, in addition to the central finite differences, with those of the standard high-order spectral element approach. Our results show, through all the test cases, that the finite element with the cubic basis-spline function is more accurate than the other vertical discretization methods at moderate computational cost. Furthermore, grid dependency studies in the tests with and without orography indicate that the convergence rate of the vertical discretization methods is lower than the expected level of discretization accuracy, especially in the Schär mountain test, which yields approximately first-order convergence.

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24

Gao, Yichao, Feng Jin, Xiang Wang y Jinting Wang. "Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary". Mathematical Problems in Engineering 2011 (2011): 1–23. http://dx.doi.org/10.1155/2011/210624.

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The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB). Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.

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25

Keith, Brendan. "A priori error analysis of high-order LL* (FOSLL*) finite element methods". Computers & Mathematics with Applications 103 (diciembre de 2021): 12–18. http://dx.doi.org/10.1016/j.camwa.2021.10.015.

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26

Diosady, Laslo T. y Scott M. Murman. "Scalable tensor-product preconditioners for high-order finite-element methods: Scalar equations". Journal of Computational Physics 394 (octubre de 2019): 759–76. http://dx.doi.org/10.1016/j.jcp.2019.04.047.

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27

Ainsworth, Mark. "Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods". Journal of Computational Physics 198, n.º 1 (julio de 2004): 106–30. http://dx.doi.org/10.1016/j.jcp.2004.01.004.

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28

Adjerid, Slimane, Mohammed Aiffa y Joseph E. Flaherty. "High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems". SIAM Journal on Applied Mathematics 55, n.º 2 (abril de 1995): 520–43. http://dx.doi.org/10.1137/s0036139993269345.

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29

Giani, Stefano. "High-order/ $$hp$$ -adaptive discontinuous Galerkin finite element methods for acoustic problems". Computing 95, S1 (20 de diciembre de 2012): 215–34. http://dx.doi.org/10.1007/s00607-012-0253-5.

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30

Iskandarani, M., J. C. Levin, B. J. Choi y D. B. Haidvogel. "Comparison of advection schemes for high-order h–p finite element and finite volume methods". Ocean Modelling 10, n.º 1-2 (enero de 2005): 233–52. http://dx.doi.org/10.1016/j.ocemod.2004.09.005.

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31

Lu, Hongqiang, Kai Cao, Lechao Bian y Yizhao Wu. "High-Order Mesh Generation for Discontinuous Galerkin Methods Based on Elastic Deformation". Advances in Applied Mathematics and Mechanics 8, n.º 4 (27 de mayo de 2016): 693–702. http://dx.doi.org/10.4208/aamm.2014.m618.

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AbstractIn this paper, a high-order curved mesh generation method for Discontinuous Galerkin methods is introduced. First, a regular mesh is generated. Second, the solid surface is re-constructed using cubic polynomial. Third, the elastic governing equations are solved using high-order finite element method to provide a fully or partly curved grid. Numerical tests indicate that the intersection between element boundaries can be avoided by carefully defining the elasticity modulus.

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32

Turusbekova, U. K., M. M. Muratbekov y S. A. Altynbek. "RESEARCH OF ALGORITHMS FOR SEARCHING PRIMITIVE ELEMENTS OF A FINITE FIELD OF HIGH ORDER". Herald of the Kazakh-British technical university 21, n.º 1 (25 de marzo de 2024): 85–93. http://dx.doi.org/10.55452/1998-6688-2024-21-1-85-93.

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One of the most important unsolved and notoriously difficult problems in computational finite field theory is the development of a fast algorithm for constructing primitive roots in a finite field. It is known that for many applications, instead of a primitive root, just an element of high multiplicative order is sufficient. Such applications include, but are not limited to, cryptography, coding theory, pseudorandom number generation, and combinatorial schemes. Explicit constructions of high-order elements usually rely on combinatory methods that can provide a provable lower bound on the order, but this does not compute the exact order. Its execution usually implies knowledge of the factorization of the order. Ideally, we should be able to get a primitive element for any finite field in a reasonable amount of time. However, if the simple factorization of the group order is unknown, it is difficult to achieve the goal. Thus, we set the task of constructing an element, probably of a high order. This article discusses various algorithms that find a high-order element for general or special finite fields. This work also represents another contribution to the theory of Gauss periods over finite fields and their generalizations and analogues, which have already proven their usefulness for a number of different applications.

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33

Dziuk, Gerhard y Charles M. Elliott. "Finite element methods for surface PDEs". Acta Numerica 22 (2 de abril de 2013): 289–396. http://dx.doi.org/10.1017/s0962492913000056.

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In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit surface methods using level set descriptions of the surface, unfitted finite element methods and diffuse interface methods. In order to formulate the methods we present the necessary geometric analysis and, in the context of evolving surfaces, the necessary transport formulae. A wide variety of equations and applications are covered. Some ideas of the numerical analysis are presented along with illustrative numerical examples.

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34

Jones, Derrick y Xu Zhang. "A high order immersed finite element method for parabolic interface problems". ITM Web of Conferences 29 (2019): 01007. http://dx.doi.org/10.1051/itmconf/20192901007.

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We present a high order immersed finite element (IFE) method for solving 1D parabolic interface problems. These methods allow the solution mesh to be independent of the interface. Time marching schemes including Backward-Eulerand Crank-Nicolson methods are implemented to fully discretize the system. Numerical examples are provided to test the performance of our numerical schemes.

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35

Nshimiyimana, J. D., F. Plumier, C. Ndagije, J. Gyselinck y C. Geuzain. "High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers". Advanced Electromagnetics 9, n.º 1 (20 de marzo de 2020): 49–58. http://dx.doi.org/10.7716/aem.v9i1.1245.

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Coupled problems result in very stiff problems whose char- acteristic parameters differ with several orders in magni- tude. For such complex problems, solving them monolithi- cally becomes prohibitive. Since nowadays there are op- timized solvers for particular problems, solving uncoupled problems becomes easy since each can be solved indepen- dently with its dedicated optimized tools. Therefore the co-simulation of the sub-problems solvers is encouraged. The design of the transmission coupling conditions between solvers plays a fundamental role. The current paper ap- plies the waveform relaxation methods for co-simulation of the finite element and circuit solvers by also investigating the contribution of higher order integration methods. The method is illustrated on a coupled finite element inductor and a boost converter and focuses on the comparison of the transmission coupling conditions based on the waveform iteration numbers between the two sub-solvers. We demon- strate that for lightly coupled systems the dynamic iterations between the sub-solvers depends much on the inter- nal integrators in individual sub-solvers whereas for tightly coupled systems it depends also to the kind of transmission coupling conditions.

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36

Zhang, Xiaodi. "High order interface-penalty finite element methods for elasticity interface problems in 3D". Computers & Mathematics with Applications 114 (mayo de 2022): 161–70. http://dx.doi.org/10.1016/j.camwa.2022.03.044.

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37

Lehrenfeld, Christoph. "High order unfitted finite element methods on level set domains using isoparametric mappings". Computer Methods in Applied Mechanics and Engineering 300 (marzo de 2016): 716–33. http://dx.doi.org/10.1016/j.cma.2015.12.005.

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38

Sehlhorst, H. G., R. Jänicke, A. Düster, E. Rank, H. Steeb y S. Diebels. "Numerical investigations of foam-like materials by nested high-order finite element methods". Computational Mechanics 45, n.º 1 (18 de septiembre de 2009): 45–59. http://dx.doi.org/10.1007/s00466-009-0414-3.

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39

Li, Maojun y Aimin Chen. "High order central discontinuous Galerkin-finite element methods for the Camassa–Holm equation". Applied Mathematics and Computation 227 (enero de 2014): 237–45. http://dx.doi.org/10.1016/j.amc.2013.11.016.

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40

Deng, Quanling, Victor Ginting y Bradley McCaskill. "Construction of locally conservative fluxes for high order continuous Galerkin finite element methods". Journal of Computational and Applied Mathematics 359 (octubre de 2019): 166–81. http://dx.doi.org/10.1016/j.cam.2019.03.049.

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41

Gawlik, Evan S. y Adrian J. Lew. "High-order finite element methods for moving boundary problems with prescribed boundary evolution". Computer Methods in Applied Mechanics and Engineering 278 (agosto de 2014): 314–46. http://dx.doi.org/10.1016/j.cma.2014.05.008.

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42

Sherwin, Spencer J. y George Em Karniadakis. "A new triangular and tetrahedral basis for high-order (hp) finite element methods". International Journal for Numerical Methods in Engineering 38, n.º 22 (30 de noviembre de 1995): 3775–802. http://dx.doi.org/10.1002/nme.1620382204.

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43

Huang, Weijie, Weijun Ma, Liang Wei y Zhiping Li. "High‐order dual‐parametric finite element methods for cavitation computation in nonlinear elasticity". Numerical Methods for Partial Differential Equations 36, n.º 5 (10 de enero de 2020): 1012–27. http://dx.doi.org/10.1002/num.22462.

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44

Attanayake, Champike, So-Hsiang Chou null y Quanling Deng. "High-Order Enriched Finite Element Methods for Elliptic Interface Problems with Discontinuous Solutions". International Journal of Numerical Analysis and Modeling 20, n.º 6 (junio de 2023): 870–95. http://dx.doi.org/10.4208/ijnam2023-1038.

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45

夏, 有伟. "High Order Central Discontinuous Galerkin-Finite Element Methods for the abcd Boussinesq System". Advances in Applied Mathematics 12, n.º 10 (2023): 4288–99. http://dx.doi.org/10.12677/aam.2023.1210422.

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46

Followell, David, Salvatore Liguore, Rigo Perez, W. Yates y William Bocchi. "Computer-Aided Reliability Finite Element Methods". Journal of the IEST 34, n.º 5 (1 de septiembre de 1991): 46–52. http://dx.doi.org/10.17764/jiet.2.34.5.9720337614871186.

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Finite element analyses (FEA) have emerged as a process for assessing stresses and strains in electronic equipment in order to compute the expected structural life. However, potential pitfalls may compromise accuracy. Guidelines have been established to improve the accuracy of these results. A method has been outlined that allows simplified linear FEAs to be used instead of the more complex elastic-plastic nonlinear FEA. Guidelines for mesh generation have been established to eliminate arithmetic errors caused when materials with large stiffness differences are adjacent to each other. The accuracy of FEAs when dealing with very small dimensions has been verified. Procedures for combining various loadings in order to predict life have been established for materials that exhibit stress relaxation and for those that do not. With these guidelines, FEAs can be an effective tool to predict the structural life of electronic equipment.

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47

Feng, Gang Chen and Minfu. "Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements". Advances in Applied Mathematics and Mechanics 10, n.º 1 (junio de 2018): 77–99. http://dx.doi.org/10.4208/aamm.2016.m1182.

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48

Houston, Paul, Christoph Schwab y Endre Süli. "Stabilizedhp-Finite Element Methods for First-Order Hyperbolic Problems". SIAM Journal on Numerical Analysis 37, n.º 5 (enero de 2000): 1618–43. http://dx.doi.org/10.1137/s0036142998348777.

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Farthing, Matthew W., Christopher E. Kees y Cass T. Miller. "Mixed finite element methods and higher-order temporal approximations". Advances in Water Resources 25, n.º 1 (enero de 2002): 85–101. http://dx.doi.org/10.1016/s0309-1708(01)00022-7.

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Lin, T., Y. Lin, W. W. Sun y Z. Wang. "Immersed finite element methods for 4th order differential equations". Journal of Computational and Applied Mathematics 235, n.º 13 (mayo de 2011): 3953–64. http://dx.doi.org/10.1016/j.cam.2011.01.041.

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