International Journal for Numerical Methods in Engineering · 2020 · 11 citations · 59 references
ComputingComputational EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisError EstimationFinite Element DiscretizationFinite Element FormulationSolid Mechanics ApplicationsConvergenceEnergy Norm Error AnalysisFinite Element ModelingHomogenizationNonconforming Finite ElementsNumerical Homogenization
Abstract 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 of in the energy norm. The nonconforming FEM shares the same property while the FEM converges at . Yet, the AFEM is on par with the FEM for certain homogenization problems.
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