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

Abstract

© 2019 Wiley Periodicals, Inc. Collocation with triquadratic C1-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.