Finite element method for a nonsmooth elliptic equation

Abstract

In this paper, we study the finite element method for a non-smooth elliptic equation. Error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis. We also propose two algorithms for solving the underlying equation. Numerical experiments are employed to confirm our error estimations and the efficiency of our algorithms.

Keywords

Finite element method / nonsmooth elliptic equation / a priori error estimate / a posteriori error estimate / superconvergence analysis / active set method

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