Adaptive Mixed Finite Element Method for Elliptic Problems with Concentrated Source Terms

An adaptive mixed finite element method using the Lagrange multiplier technique is used to solve elliptic problems with delta Dirac source terms. The problem arises in the use of Chow-Anderssen linear functional methodology to recover coefficients locally in parameter estimation of an elliptic equation from a pointwise measurement. In this article, we used a posteriori error estimator based on averaging technique as refinement indicators to produce a cycle of mesh adaptation, which is experimentally shown to capture singularity phenomena. Our numerical result showed that the adaptive refinement process successfully refines elements around the centre of the source terms and show that the global error estimation is better than uniform refinement process in terms of computation time.