Maximum‐norm a posteriori error bounds for a collocation method applied to a singularly perturbed reaction–diffusion problem in three dimensions

Abstract

Collocation with triquadratic C 1 -splines for a singularly perturbed reaction-diffusion problem in three dimension is studied. A posteriori error bound in the maximum norm is derived for the collocation method on arbitrary tensor-product meshes which is robust in the perturbation parameter. Numerical results are presented that support our theoretical estimate. KEYWORDS a posteriori error bound, collocation method, Green's function, maximum norm, reaction-diffusion problems, singular perturbation 1 * 2 q] [i]