The discontinuous enrichment method

We propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a non-conforming field that is added to it. The enrichment contains free-space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field, Continuity of the enrichment across element interfaces is enforced weakly by Lagrange multipliers. In this manner, we expect to attain high coarse-mesh accuracy without significant degradation of conditioning, assuring good performance of the computation at any mesh resolution. Examples of application to acoustics and advection-diffusion are presented. (C) 2001 Elsevier Science B,V. All rights reserved.