An Extended Galerkin analysis in finite element exterior calculus
arXiv:2101.09735 · doi:10.1090/mcom/3707
Abstract
For the Hodge--Laplace equation in finite element exterior calculus, we introduce several families of discontinuous Galerkin methods in the extended Galerkin framework. For contractible domains, this framework utilizes seven fields and provides a unifying inf-sup analysis with respect to all discretization and penalty parameters. It is shown that the proposed methods can be hybridized as a reduced two-field formulation.
References in corpus (12)
- Finite element exterior calculus: from Hodge theory to numerical stability
- Mixed finite element methods for linear elasticity with weakly imposed symmetry
- Finite elements for symmetric tensors in three dimension
- Finite element differential forms on cubical meshes
- Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
- Some convergence and optimality results of adaptive mixed methods in finite element exterior calculus
- Finite element exterior calculus for parabolic problems
- Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors
- Generalized Finite Element Systems for smooth differential forms and Stokes problem
- Hybridization and postprocessing in finite element exterior calculus
- Finite Element Exterior Calculus for Evolution Problems
- A Unified Study of Continuous and Discontinuous Galerkin Methods
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- A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian
- New Discontinuous Galerkin Algorithms and Analysis for Linear Elasticity with Symmetric Stress Tensor