Performance assessment of the augmented finite element method for the modeling of weak discontinuities

This article investigates the convergence properties of the augmented finite element method (AFEM). The AFEM is here used to model weak discontinuities independently of the underlying mesh. One noticeable advantage of the AFEM over other partition of unity methods is that it does not introduce additional global unknowns. Numerical 2D experiments illustrate the performance of the method and draw comparisons with the finite element method (FEM) and the nonconforming FEM. It is shown that the AFEM converges with an error ofO(h0.5)in the energy norm. The nonconforming FEM shares the same property while the FEM converges atO(h). Yet, the AFEM is on par with the FEM for certain homogenization problems.

Automated summary

This article investigates the convergence properties of the augmented finite element method (AFEM), showing that it converges with an error of O(h^0.5) in the energy norm. The AFEM has the advantage of not introducing additional global unknowns compared to other partition of unity methods, and is on par with the finite element method for certain homogenization problems.