Numerical Analysis Group Research Report NA-94/5

Analysis of the cell vertex finite volume method for the Cauchy Riemann equations

M. Vanmaele, K. W. Morton, Endre Süli and A. Borzi

(Accepted for publication in SIAM Journal on Numerical Analysis.)

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