Cell Boundary Element Methods for Convection-diffusion Equations

The purpose of the paper is to introduce a novel cell boundary element (CBE) method for the convection dominated diffusion equation. The CBE method can be viewed as a Petrov-Galerkin type method defined on the skeleton of a mesh. The proposed method utilizes continuity of normal flux on each inter-element boundary. By constructing a local basis (mesh-oriented element) that is dependent upon the orientation of the mesh we could obtain a stable non-oscillatory numerical scheme. We also consider a local basis (windoriented element) which incorporates the wind direction. Numerical examples are presented to compare various elements with the existing method such as the streamline diffusion method (SUPG).