A higher‐order discontinuous enrichment method for the solution of high péclet advection–diffusion problems on unstructured meshes

Abstract

AbstractA higher‐order discontinuous enrichment method (DEM) with Lagrange multipliers is proposed for the efficient finite element solution on unstructured meshes of the advection–diffusion equation in the high Péclet number regime. Following the basic DEM methodology, the usual Galerkin polynomial approximation is enriched with free‐space solutions of the governing homogeneous partial differential equation (PDE). In this case, these are exponential functions that exhibit a steep gradient in a specific flow direction. Exponential Lagrange multipliers are introduced at the element interfaces to weakly enforce the continuity of the solution. The construction of several higher‐order DEM elements fitting this paradigm is discussed in detail. Numerical tests performed for several two‐dimensional benchmark problems demonstrate their computational superiority over stabilized Galerkin counterparts, especially for high Péclet numbers. Copyright © 2009 John Wiley & Sons, Ltd.