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Locking-free DGFEM for elasticity problems in polygons 总被引:1,自引:0,他引:1
The h-version of the discontinuous Galerkin finite element method(h-DGFEM) for nearly incompressible linear elasticity problemsin polygons is analysed. It is proved that the scheme is robust(locking-free) with respect to volume locking, even in the absenceof H2-regularity of the solution. Furthermore, it is shown thatan appropriate choice of the finite element meshes leads torobust and optimal algebraic convergence rates of the DGFEMeven if the exact solutions do not belong to H2. 相似文献
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Thomas P. Wihler. 《Mathematics of Computation》2006,75(255):1087-1102
An adaptive discontinuous Galerkin finite element method for linear elasticity problems is presented. We develop an a posteriori error estimate and prove its robustness with respect to nearly incompressible materials (absence of volume locking). Furthermore, we present some numerical experiments which illustrate the performance of the scheme on adaptively refined meshes.
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Thomas Wihler 《PAMM》2011,11(1):11-14
Suitable continuous Sobolev embeddings are applied in order to derive smoothness estimators for adaptive hp-refinements in the context of hp-finite element methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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An hp‐adaptive Newton‐Galerkin finite element procedure for semilinear boundary value problems 下载免费PDF全文
Mario Amrein Jens Markus Melenk Thomas P. Wihler 《Mathematical Methods in the Applied Sciences》2017,40(6):1973-1985
In this paper, we develop an hp‐adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction‐type adaptive Newton method and an hp‐version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully hp‐adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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The aim of this paper is to develop an hp-version a posteriori error analysis for the time discretization of parabolic problems by the continuous Galerkin (cG) and
the discontinuous Galerkin (dG) time-stepping methods, respectively. The resulting error estimators are fully explicit with
respect to the local time-steps and approximation orders. Their performance within an hp-adaptive refinement procedure is illustrated with a series of numerical experiments. 相似文献
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Summary. We analyze mixed hp-discontinuous Galerkin finite element methods (DGFEM) for Stokes flow in polygonal domains. In conjunction with geometrically refined quadrilateral meshes and linearly increasing approximation orders, we prove that the hp-DGFEM leads to exponential rates of convergence for piecewise analytic solutions exhibiting singularities near corners.
Mathematics Subject Classification (2000):65N30 相似文献
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Adaptive pseudo‐transient‐continuation‐Galerkin methods for semilinear elliptic partial differential equations 下载免费PDF全文
Mario Amrein Thomas P. Wihler 《Numerical Methods for Partial Differential Equations》2017,33(6):2005-2022
In this article, we investigate the application of pseudo‐transient‐continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with possible singular perturbations. We will outline a residual reduction analysis within the framework of general Hilbert spaces, and, subsequently, use the PTC‐methodology in the context of finite element discretizations of semilinear boundary value problems. Our approach combines both a prediction‐type PTC‐method (for infinite dimensional problems) and an adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully adaptive PTC ‐Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for different examples.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2005–2022, 2017 相似文献