Analysis of a Fourth Order Scheme and Application of Local Defect Correction Method

Abstract

This paper provides a new application similar to the Local Defect Correction (LDC) technique to solve Poisson problem −u ′′ (x) = f (x) with Dirichlet boundary conditions. The exact solution is supposed to have high activity in some region of the domain. LDC is combined with a fourth order compact scheme which is recently developed in Abbas (Num. Meth. Partial differential equations, 2013). Numerical tests illustrate the interest of this application.