Numerical computations of the PCD method

Abstract

The PCD (piecewise constant distributions) method is a discretization technique of the boundary value problems in which the unknown distribution and its derivatives are represented by piecewise constant distributions but on distinct meshes. It has the advantage of producing the most sparse stiffness matrix resulting from the approximate problem. In this contribution, we propose a general PCD triangulation by combining rectangular elements and triangular elements. We also apply this discretization technique for the elasticity problem. We end with presentation of numerical results of the proposed method for the 2D diffusion equation.

Keywords

• Boundary value problem
• discretization technique
• PCD method
• compact schemes
• approximate solution
• most sparse stiffness matrix
• $O(h)$-convergence rate