Adaptive mesh construction for a class of singularly perturbed differential equations

Dr. Naresh Chadha

April 13, 2010, 3:30 p.m. HS 13

Singularly perturbed differential equations arise in many practical applications, such as flow in porous media, semiconductor device modeling, ion transport across biological membranes. In general, these types of problems exhibit a layer behavior; and commonly used numerical methods may fail to resolve these layers. To solve such problems numerically in a reliable and efficient way, one has to use locally refined meshes.

In this talk, we will discuss the convergence analysis of a r-adaptive method based on equidistribution principle. The problems considered are singularly perturbed one-dimensional convection-diffusion and reaction-diffusion problems. It is proved that starting from a uniform mesh, the algorithm used provides a layer-adapted mesh on which the computed solution is sufficiently accurate. The issues related to extending equidistribution principle to higher dimensions will also be discussed.