The discontinuous enrichment method

Charbel Farhat (1) , Isaac Harari (2) , Leopoldo Franca (3)

1 University of Colorado [Boulder]
2 TAU - Tel Aviv University
3 University of Colorado [Denver]

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.

Mots clés: Finite elements; Discontinuous enrichment; Acoustics; Advection-diffusion

Domaines: Mécanique des structures [physics.class-ph]

Charbel Farhat, Isaac Harari, Leopoldo Franca. The discontinuous enrichment method. Computer Methods in Applied Mechanics and Engineering, 2001, 190 (48), pp.6455-6479. ⟨10.1016/S0045-7825(01)00232-8⟩. ⟨hal-02012889⟩