Computer Methods in Applied Mechanics and Engineering
A new family of mixed finite elements in IR3
Numerische Mathematik
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Mixed finite element methods for stationary incompressible magneto–hydrodynamics
Numerische Mathematik
Applied Numerical Mathematics
A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems
SIAM Journal on Numerical Analysis
Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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In this work we propose stabilized finite element methods for Stokes@?, Maxwell@?s and Darcy@?s problems that accommodate any interpolation of velocities and pressures. We briefly review the formulations we have proposed for these three problems independently in a unified manner, stressing the advantages of our approach. In particular, for Darcy@?s problem we are able to design stabilized methods that yield optimal convergence both for the primal and the dual problems. In the case of Maxwell@?s problem, the formulation we propose allows one to use continuous finite element interpolations that converge optimally to the continuous solution even if it is non-smooth. Once the formulation is presented for the three model problems independently, we also show how it can be used for a problem that combines all the operators of the independent problems. Stability and convergence is achieved regardless of the fact that any of these operators dominates the others, a feature not possible for the methods of which we are aware.