A posteriori error estimators for elliptic equations with discontinuous coefficients. (English) Zbl 0997.65123

Petzoldt, Martin

Adv. Comput. Math. 16, No. 1, 47-75 (2002).

This paper deals with the elliptic problem \(\nabla(k(x)\nabla u)= f\in L^2(\Omega)\), \(\Omega\subset \mathbb{R}^d\), \(d= 2,3\), where \(k\) is a piecewise constant and positive on polygonal (polyhedral) subdomains, and mixed boundary conditions are given. A posteriori error estimators for the mentioned problems are analyzed. The error estimators can be shown to be robust reliable and efficient for quasi-monotonically distributed coefficients. In the nonquasi-monotone case robustness can not be proven. Some numerical tests are presented.

Reviewer: Pavol Chocholatý (Bratislava)

MSC:

65N15	Error bounds for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
35R05	PDEs with low regular coefficients and/or low regular data

Keywords:

elliptic equations; discontinuous coefficients; a posteriori error estimators; numerical tests

Software:

pdelib