A Note on Galerkin's Method for Nonlinear Equations.
Satzish Shirali (1970)
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Satzish Shirali (1970)
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Mitsuhiro T. Nakao (1985)
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M. Marion, R. Temam (1990)
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Satish Shirali (1969)
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J. A. Nitsche (1978)
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Niels Jacob, Bernd Schomburg (1986)
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Ohm, Mi Ray, Lee, Hyun Young, Shin, Jun Yong (2010)
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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...
J.J. Blair (1972)
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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...