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NEGATIVE NORM ESTIMATES AND SUPERCONVERGENCE IS GALEBKIN METHODS FOR PARABOLIC PROBLEMS

机译：负惯性估计和超收敛是抛物问题的GaLEBKIN方法

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摘要

The purpose is to show how known negative norm error estimates for Galerkin-finite element type methods applied to the Dirichlet problem for second order elliptic equations can be carried over to initial-boundary value problems for nonhomogeneous parabolic equations. Attempts are then made to describe how such estimates may be used to prove superconvergence of a number of procedures for evaluating point values of the exact solution and its derivatives. These applications include in particular the case of one space dimension with continuous, piecewise polynomial approximating subspaces, where methods proposed by Douglas, Dupont and Wheeler are analyzed. Further, in higher dimensions the application of an averaging procedure by Bramble and Schatz is discussed for elements which are uniform in the interior and in the non-uniform case, a method employing a local Green's function considered by Louis and Natterer.

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作者
Vidar Tnomee;
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年度 1980
页码 1-37
总页数 37
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Galerkin method; Norms; Parabolic differential equations; Convergence; Error analysis; Estimates; Finite element method; Set theory; Greens function; Sweden;

机译：Galerkin方法;规范;抛物微分方程;收敛;误差分析;估计;有限元法;集合论;格林函数;瑞典;

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2. On Superconvergence Results and Negative Norm Estimates for a Unidimensional Single Phase Stefan Problem [J] . L.Jones, A.K.Pani Numerical Functional Analysis and Optimization . 1995,第1a2期

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3. L~∞(L~2) and L~∞(H~1) norms error estimates in finite element method for linear parabolic interface problems [J] . Deka B., Sinha R.K. Numerical Functional Analysis and Optimization . 2011,第1a3期

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4. Global Superconvergence Estimates of Petrov-Galerkin Methods for Hyperbolic Equations [C] . Yang Bo 2nd International Workshop on Database Technology and Applications . 2010

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5. Maximum Norm Regularity of Implicit Difference Methods for Parabolic Equations. [D] . Pruitt, Michael. 2011

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6. Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems [O] . Yuelong Tang, Yuchun Hua -1

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7. Parabolic Partial Integro-Differential Equations: Superconvergence Estimates and Applications [O] . Pinto Luís Miguel Dias 2014

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NEGATIVE NORM ESTIMATES AND SUPERCONVERGENCE IS GALEBKIN METHODS FOR PARABOLIC PROBLEMS

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