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An Adaptive Finite Element Method for a Linear Elliptic Equation with Variable Coefficients
Author(s) -
Dörfler W.,
Wilderotter O.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200007)80:7<481::aid-zamm481>3.0.co;2-5
Subject(s) - estimator , finite element method , bounded function , a priori and a posteriori , polygon mesh , mathematics , discontinuity (linguistics) , convergence (economics) , elliptic curve , adaptive algorithm , variable (mathematics) , computer science , mathematical optimization , algorithm , mathematical analysis , geometry , philosophy , statistics , physics , epistemology , economics , thermodynamics , economic growth
We study the adaptive finite element method to solve linear elliptic boundary value problems on bounded domains in ℝ 2 . For this we first prove a posteriori error estimates that carefully take data error into account and show convergence of an adaptive algorithm. Then we propose an adaptive method that may start from very coarse meshes. A numerical example underlines the necessity of monitoring the data error in applications. Moreover, we can show that the a posteriori error bound of our proposed error estimator will (in a simple model situation) not depend on jumps in the coefficient of the main part of the equation when the lines of discontinuity are resolved by the mesh.