Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems
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摘要
We present guaranteed and computable both sided error bounds for the discontinuous Galerkin (DG) approximations of elliptic problems. These estimates are derived in the full DG-norm on purely functional grounds by the analysis of the respective differential problem, and thus, are applicable to any qualified DG approximation. Based on the triangle inequality, the underlying approach has the following steps for a given DG approximation: (1) computing a conforming approximation in the energy space using the Oswald interpolation operator, and (2) application of the existing functional a posteriori error estimates to the conforming approximation. Various numerical examples with varying difficulty in computing the error bounds, from simple problems of polynomial-type analytic solution to problems with analytic solution having sharp peaks, or problems with jumps in the coefficients of the partial differential equation operator, are presented which confirm the efficiency and the robustness of the estimates.
论文关键词:65N15,65N30,A posteriori error estimates,Discontinuous Galerkin method,Elliptic partial differential equation
论文评审过程:Available online 13 August 2008.
论文官网地址:https://doi.org/10.1016/j.cam.2008.08.015