Adaptive mixed finite element method for elliptic problems with concentrated source terms

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