A local differential quadrature scheme for solving the Poisson equation with strong discontinuities

In this paper, the effect of strong discontinuities on the solution of a Dirichlet problem governed by the Poisson equation is investigated. The numerical solution is obtained using the local differential quadrature method (LDQM), in two ways: one employs the conventional LDQM approach without any discontinuity treatment, and the second uses a new LDQM technique to treat the discontinuity, which is based on reducing the propagation of errors arising from the discontinuity. The results show that the LDQM solution achieves greater accuracy when the discontinuity treatment technique is used.