Finite element exterior calculus, homological techniques, and applications
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- Type
- article
- Published
- 2006-05-01
- Cited by
- 1,111
- References
- 103
- Access
- Open access
- OpenAlex
- https://openalex.org/W2138486270
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:122763537
Keywords
Mathematics, Finite element method, Vector calculus, Extended finite element method, Mixed finite element method
References
- MULTIGRID METHOD FORH(DIV) IN THREE DIMENSIONS
- The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations
- An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term
- The Mathematical Theory of Finite Element Methods
- Supersymmetry and equivariant de Rham theory
- Differential complexes and numerical stability
- Geometric Integration Theory
- Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations
- Mixed and hybrid finite element methods
- On the convergence of eigenvalues for mixed formulations
- Perturbation theory for linear operators
- Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms
- On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers
- Error estimates for mixed methods
- Mixed and Hybrid Finite Element Methods
- Dual hybrid methods for the elasticity and the Stokes problems: a unified approach
- Mechanical conditions for stability and optimal convergence of mixed finite elements for linear plane elasticity
- An equilibrium stress field model for finite element solutions of two-dimensional elastostatic problems
- A New Convergence Proof for the Multigrid Method Including the V-Cycle
- Multilevel iterative methods for mixed finite element discretizations of elliptic problems
Cited by
- Least Squares Ranking on Graphs, Hodge Laplacians, Time Optimality, and Iterative Methods
- Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
- Computation of Maxwell's equations on manifold using implicit DEC scheme
- Linear and Nonlinear Elastostatics Complexes
- Eulerian Geometric Discretizations of Manifolds and Dynamics
- ELLIPTIC EQUATIONS WITH SINGULARITIES: A PRIORI ANALYSIS AND NUMERICAL APPROACHES
- Real Homology Cohomology and Harmonic Cochains, Least Squares, and Diagonal Dominance
- From Raviart-Thomas to HDG: a personal voyage
- Periodic Table of the Finite Elements
- Bases de fonctions sur les variétés
- Mimetic spectral element method; a discretization of geometry and physics
- Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations
- Stokes elements on cubic meshes yielding divergence-free approximations
- A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics
- Discrete Derivatives of Vector Fields on Surfaces -- An Operator Approach
- Explorations of Infinitesimal Inverse Spectral Geometry
- Full and Model-Reduced Structure-Preserving Simulation of Incompressible Fluids
- A residual-based a posteriori error estimator for the plane linear elasticity problem with pure traction boundary conditions
- A mixed discontinuous Galerkin method for the time harmonic elasticity problem with reduced symmetry
- Polynomial extension operators for H1, H(curl) and H(div)-spaces on a cube
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