Dynamically Adapted Mesh Construction for the Efficient Numerical Solution of a Singular Perturbed Reaction-diffusion-advection Equation

Abstract

This work develops a theory of the asymptotic-numerical investigation of the moving fronts in reaction-diffusion-advection models. By considering the numerical solution of the singularly perturbed Burgers’s equation we discuss a method of dynamically adapted mesh construction that is able to significantly improve the numerical solution of this type of equations. For the construction we use a priori information that is based on the asymptotic analysis of the problem. In particular, we take into account the information about the speed of the transition layer, its width and structure. Our algorithms are able to reduce significantly complexity and enhance stability of the numerical calculations in comparison with classical approaches for solving this class of problems. The numerical experiment is presented to demonstrate the effectiveness of the proposed method.The article is published in the authors’ wording.

Keywords

• singularly perturbed
• interior layer
• dynamically adapted mesh