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The discontinuous enrichment method. (English) Zbl 1002.76065
Summary: 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 a 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.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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