ANALYSIS OF THE CELL VERTEX FINITE-VOLUME METHOD FOR THE CAUCHY-RIEMANN EQUATIONS

This paper initiates a study of finite volume methods for linear first -order elliptic systems by performing a stability and convergence anal ysis of the cell Vertex approximation of the Cauchy-Riemann equations. The approach is based on reformulating the scheme as a Petrov-Galerki n finite element method with continuous bilinear trial functions and p iecewise constant test functions. Optimal error bounds are derived in a mesh-dependent norm, and the counting problem which may occur due to geometry and boundary conditions is considered.