Algorithms For A Vertex-Centered Covolume Method For Indefinite Elliptic Problem

It's well known that the covolume methods (finite volume el-ement methods) are widely and successfully used in solving many mathematical-physical problems due to their simplicity and local conservation properties in recent years. In this paper, we use covol-ume method to discrete second order norisyrnmetric and indefinite elliptic problem on a polygonal domain (possibly nonconvex). For solving the corresponding discretization equation, there are few re-sults on the construction of efficient solvers. Most existing results only presented the related error estimate for a concrete problem discretized by covolume methods. In this paper, hierarchical basis method, domain decomposition method and precondtioned GMRES method are constructed. The convergence of these method are also verified.