A direct finite-difference scheme for solving PDEs over general two-dimensional regions Original Research Article

Classical finite-difference methods apply only over regions that are rectangular or decomposed in several rectangular subdomains. We call a finite-difference scheme direct if it can be applied over any region decomposed using a logically-rectangular grid. We introduce a new second-order-accurate direct scheme to solve boundary-value problems. Numerical results confirm the second-order accuracy on smooth grids and even some very distorted grids. However, on some severely distorted grids, the method does not perform well.