A two-level enriched finite element method for a mixed problem

The simplest pair of spaces P1/P0 is made inf-sup stable for the mixed form of the Darcy equation. The key ingredient is enhance the finite element spaces inside a PetrovGalerkin framework with functions satisfying element-wise local Darcy problems with right hand sides depending on the residuals over elements and edges. The enriched method is symmetric, locally mass conservative and keeps the degrees of freedom of the original interpolation spaces. First, we assume local enrichments exactly computed and we prove uniqueness and optimal error estimates in natural norms. Then, a low cost two-level finite element method is proposed to effectively obtain enhancing basis functions. The approach lays on a two-scales numerical analysis and shows that well-posedness and optimality is kept despite of the second level numerical approximation. Several numerical experiments validate the theoretical results and compares (favourably in some cases) our results with the classical Raviart-Thomas ele...

• Type: Journal
• Year: 2011
• Where: MOC
• Authors: Alejandro Allendes, Gabriel R. Barrenechea, Erwin Hernández, Frédéric Valentin
• Keywords: Element-wise Local Darcy, Intelligent Agents, MOC 2011, Two-level finite Element, finite Element