Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces

DOI10.1007/s10208-012-9119-7zbMath1263.65114arXiv1005.4455OpenAlexW2034024171WikidataQ125717531 ScholiaQ125717531MaRDI QIDQ454134

Michael Holst, Ari Stern

Publication date: 1 October 2012

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.4455

zbMATH Keywords

mixed finite elementsisoparametric finite elementsfinite element exterior calculusgeometric finite element methodsHilbert complexsurface finite elementsvariational crimes

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) de Rham theory in global analysis (58A12)

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Uses Software

• SG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
• An algorithm for evolutionary surfaces
• Finite element approximations to surfaces of prescribed variable mean curvature
• Mixed finite elements in \(\mathbb{R}^3\)
• Hilbert complexes
• Curved finite element methods for the solution of singular integral equations on surfaces in \(R^3\)
• Introduction to differentiable manifolds.
• Convergence of a finite element method for non-parametric mean curvature flow
• Finite element exterior calculus, homological techniques, and applications
• Computation of geometric partial differential equations and mean curvature flow
• Finite elements on evolving surfaces
• A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS
• Finite element exterior calculus: from Hodge theory to numerical stability
• Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form
• Electromagnetic Theory and Computation
• Finite Elemente
• Smoothed projections in finite element exterior calculus
• An Adaptive Finite Element Method for the Laplace–Beltrami Operator on Implicitly Defined Surfaces
• Adaptive numerical treatment of elliptic systems on manifolds

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