Abstract

We introduce an adaptively weighted Galerkin approach for elliptic problems where diffusion is dominated by strong convection or reaction terms. In such problems, standard Galerkin approximations can have unacceptable oscillatory behavior near boundaries unless the computational mesh is sufficiently fine. Here we show how adaptively weighting the equations within the variational problem can increase accuracy and stability of solutions on under-resolved meshes. Rather than relying on specialized finite elements or meshes, the idea here sets a flexible and robust framework where the metric of the variational formulation is adapted by an approximate solution. We give a general overview of the formulation and an algorithmic structure for choosing weight functions. Numerical examples are presented to illustrate the method.

Keywords

Mathematical Subject Classification 2010

Milestones

Authors