A General Finite Difference Method for Arbitrary Meshes

摘要

A two-dimensional finite difference technique for irregular meshes is suggested to obtain derivatives up to the order of two. The technique enjoys two major advantages: (1) avoidance of singularity in derivative coefficient matrix, and (2) better accuracy of derivatives than that obtained previously. For square meshes general derivative expressions for arbitrary meshes reduce to the usual central finite difference formulae. Example problems solved are a Poisson equation and the large deflection of a square flat membrane; the solutions compare quite well with results obtained elsewhere. For problems with higher order derivative terms, two possible approaches are discussed. (Author)