On Weak Residual Error Estimation

A general framework for weak residual error estimators applying to various types of boundary value problems in connection with finite element and finite volume approximations is developed. Basic ideas commonly shared by various applications in error estimation and adaptive computation are presented and illustrated. Some numerical results are given to show the effectiveness and efficiency of the estimators.

[1]  Zhiqiang Cai,et al.  On the finite volume element method , 1990 .

[2]  W. Rheinboldt,et al.  Error Estimates for Adaptive Finite Element Computations , 1978 .

[3]  Leszek Demkowicz,et al.  Toward a universal h-p adaptive finite element strategy , 1989 .

[4]  W. Rheinboldt.  On the computation of multi-dimensional solution manifolds of parametrized equations , 1988 .

[5]  D. Rose,et al.  Some errors estimates for the box method , 1987 .

[6]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[7]  Ivo Babuška,et al.  The post-processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements , 1984 .

[8]  A. Aziz,et al.  A weighted least squares method for the backward-forward heat equation , 1991 .

[9]  Joseph E. Flaherty,et al.  a posteriori Error estimation for triangular and tetrahedral quadratic elements using interior residuals , 1992 .

[10]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[11]  W. Rheinboldt,et al.  A Posteriori Error Estimates for Parametrized Nonlinear Equations , 1990 .

[12]  R. Bank,et al.  Some a posteriori error estimators for elliptic partial differential equations , 1985 .

[13]  J. Oden,et al.  Toward a universal h - p adaptive finite element strategy: Part 2 , 1989 .

[14]  J. Tinsley Oden,et al.  Local a posteriori error estimators for variational inequalities , 1993 .

[15]  R. Kellogg,et al.  Iterative methods for a forward-backward heat equation , 1990 .

[16]  Werner C. Rheinboldt,et al.  A posteriori finite element error estimators for indefinite elliptic boundary value problems , 1994 .

[17]  P. Lesaint,et al.  Finite element methods for symmetric hyperbolic equations , 1973 .

[18]  W. Rheinboldt.  Numerical analysis of parametrized nonlinear equations , 1986 .

[19]  R. S. Falk.  Error estimates for the approximation of a class of variational inequalities , 1974 .

[20]  Joseph E. Flaherty,et al.  Second-order finite element approximations and a posteriori error estimation for two-dimensional parabolic systems , 1988 .

[21]  J. Oden,et al.  A unified approach to a posteriori error estimation using element residual methods , 1993 .

[22]  Ivo Babuška,et al.  A Posteriori Error Estimates of Finite Element Solutions of Parametrized Nonlinear Equations , 1992 .

[23]  D. Kelly,et al.  The self‐equilibration of residuals and complementary a posteriori error estimates in the finite element method , 1984 .

[24]  Joseph E. Flaherty,et al.  A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems , 1993 .

[25]  D. Griffin,et al.  Finite-Element Analysis , 1975 .