The Cell Boundary Element Method for Elliptic Pdes-Local Error Analysis

The CBEM(cell boundary element method) was proposed for the generalized Poisson type equation ∇⋅( ∇ ) = by the author in an earlier paper [2001]. In this paper local error analysis for the CBEM with various scales of rectangular meshes is provided for the harmonic equation, that is a simplified form of the above equation. We also conjecture global error estimates and numerical experiments confirming our assertion are given. We observe that the error analysis is still valid for the generalized Poisson type equation through numerical experiments