Error estimates for the ultra weak variational formulation in linear elasticity
نویسندگان
چکیده
منابع مشابه
Error Estimates for the Ultra Weak Variational Formulation of the Helmholtz Equation
Abstract. The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation provides a variational framework suitable for discretization using plane wave solutions of the adjoint of the underlying equation. Currently convergence of the method is only proved on the boundary of the domain. However substantial computational evidence exists that shows that the method also converges throughout...
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Two-dimensional linear elasticity problems are approximately solved by a mixed finite-element method based on Raviart-Thomas-Nedelec spaces; maximum-norm error estimates of optimal rate and almost optimal regularity are derived for the displacement field, and of optimal regularity and almost optimal rate for the stress tensor. The superconvergence of the approximate displacement field to the L2...
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In this paper we investigate the feasibility of using the ultra weak variational formulation (UWVF) to solve the timeharmonic 3D elastic wave propagation problem. The UWVF is a non-polynomial volume based method that uses plane waves as basis functions which reduces the computational burden. More general, the UWVF is a special form of the discontinuous Galerkin method. As a model problem we con...
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We investigate the ultra weak variational formulation for simulating time-harmonic Maxwell problems. This study has two main goals. First, we introduce a novel derivation of the UWVF method which shows that the UWVF is an unusual version of the standard upwind discontinuous Galerkin (DG) method with a special choice of basis functions. Second, we discuss the practical implementation of an elect...
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The ultra weak variational formulation (UWVF) approach has been proposed as an effective method for solving Helmholtz problems with high wave numbers. However, for coarse meshes the method can suffer from instability. In this paper we consider computational aspects of the ultra weak variational formulation for the inhomogeneous Helmholtz problem. We introduce a method to improve the UWVF scheme...
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ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2012
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/2012025