Sharp a posteriori error estimate for elliptic equation with singular data

Abstract

We introduce two residual type a posteriori error estimators for second-order elliptic partial differential equations with its right-hand side in L^p (1<p≤2) space. Both estimators are proved to yield global upper and local lower bounds for the W^1,p seminorm of the error. We adopt the estimators as the indicators in h-mesh adaptive method to solve two typical model problems. It is verified by the numerical results that the estimators lead to optimal orders of convergence.

Keywords

L^p space / finite element method / adaptive mesh refinement / a posteriori error estimate

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg