A Combined Finite Element Scheme for Second Elliptic Problems Posted in Domains with Rough Boundaries

A finite element method(FEM) is proposed to solve second elliptic problems posted in domains with rough boundaries. We also present an FEM for elliptic problems as an extension of the original method. The optimal error estimates in the energy norm are also proved. Numerical results for second elliptic equations in regular and rough domains are presented to illustrate the efficiency of our method, respectively, which is consistent with theoretical analysis.