An equation decomposition method for the numerical solution of a fourth-order elliptic singular perturbation problem

In this article, we propose a tailored finite point method (TFPM) for the numerical solution of a type of fourth-order singular perturbation problem in two dimensions based on the equation decomposition technique. Our finite point method has been tailored based on the local exponential basis functions. Furthermore, our TFPM satisfies the discrete maximum principle automatically. Our numerical examples show that our method has second order convergence rate in energy norm as $\varepsilon\to0$. (c) 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011