Residual cutting method for elliptic boundary value problems (application to Poisson's equation)

Abstract

A new, efficient and accurate numerical method which consists of perturbed residual equation and residual L2 norm minimization is proposed for boundary value problems of elliptic partial differential equations. For example, Neumann, Dirichlet and mixed boundary value problems in a three dimensional Poisson's equation for the pressure in curved duct flow and cascade flow, are solved. Numerical results demonstrate the effectiveness, robustness and a high convergence rate of this method. Residual Cutting Method is expected to be the numerical solution method applicable to a wide range of partial differential equations with various kinds of boundary conditions.