Adaptive Grid for Parameterized Singular Perturbation Problem

Abstract

A quasilinear first order singularly perturbed boundary value problem depending on a parameter is considered. The problem is solved by a backward Euler fnitediference operator on an appropriate non-uniform mesh constructed adaptively by equidistributing a monitor function based on the solution. An error bound in the maximum norm is established theoretically whose error constants are shown to be independent of the singular perturbation parameter. The method is first-order convergent. Numerical experiment illustrates in practice the result of convergence proved theoretically.