Mortar Finite Volume Method with Adini Element for Biharmonic Problem

Abstract

In this paper, we construct and analyse a mortar finite volume method for the discretization for the biharmonic problem in $R^2$. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order $H^2$-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.