A posteriori finite element error estimators for indefinite elliptic boundary value problems∗
- 1 January 1994
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 15 (3-4) , 335-356
- https://doi.org/10.1080/01630569408816569
Abstract
A general construction technique is presented for a posteriori error estimators of finite element solutions of elliptic boundary value problems that satisfy a Gång inequality. The estimators are obtained by an element–by–element solution of ‘weak residual’ with or without considering element boundary residuals. There is no order restriction on the finite element spaces used for the approximate solution or the error estimation; that is, the design of the estimators is applicable in connection with either one of the h–p–, or hp– formulations of the finite element method. Under suitable assumptions it is shown that the estimators are bounded by constant multiples of the true error in a suitable norm. Some numerical results are given to demonstrate the effectiveness and efficiency of the approach.Keywords
This publication has 17 references indexed in Scilit:
- a posteriori Error estimation for triangular and tetrahedral quadratic elements using interior residualsInternational Journal for Numerical Methods in Engineering, 1992
- The Role of the Strengthened Cauchy–Buniakowskii–Schwarz Inequality in Multilevel MethodsSIAM Review, 1991
- Nonlinear Galerkin methods: The finite elements caseNumerische Mathematik, 1990
- Second-order finite element approximations and a posteriori error estimation for two-dimensional parabolic systemsNumerische Mathematik, 1988
- Asymptotically exact a posteriori error estimator for biquadratic elementsFinite Elements in Analysis and Design, 1987
- Some a posteriori error estimators for elliptic partial differential equationsMathematics of Computation, 1985
- The self‐equilibration of residuals and complementary a posteriori error estimates in the finite element methodInternational Journal for Numerical Methods in Engineering, 1984
- The contraction number of a multigrid method for solving the Poisson equationNumerische Mathematik, 1981
- Error Estimates for Adaptive Finite Element ComputationsSIAM Journal on Numerical Analysis, 1978
- A‐posteriori error estimates for the finite element methodInternational Journal for Numerical Methods in Engineering, 1978