Convergence of Finite Element Galerkin Approximations on Galerkin Problems
J. A. Nitsche (1978)
Publications mathématiques et informatique de Rennes
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J. A. Nitsche (1978)
Publications mathématiques et informatique de Rennes
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Thirupathi Gudi, Johnny Guzmán (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm...
Kučera, Václav
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This work is concerned with the introduction of a new numerical scheme based on the discontinuous Galerkin (DG) method. We propose to follow the methodology of higher order finite volume schemes and introduce a reconstruction operator into the DG scheme. This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. Such a procedure was proposed already in [2] based on heuristic arguments, however we provide a rigorous derivation, which justifies...
S. Champier, T. Gallouet, R. Herbin (1993/94)
Numerische Mathematik
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Vladimir Jovanović (1996)
Publications de l'Institut Mathématique
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Boško Jovanović (1992)
Publications de l'Institut Mathématique
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Boško Jovanović (1994)
Publications de l'Institut Mathématique
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Peter Hansbo, Mats G. Larson (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix–Raviart (CR) element, which in fact is obtained when one of the stabilizing parameters tends to infinity. In the case of the elasticity operator, for...
Hans-Peter Helfrich (1987)
Numerische Mathematik
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