DOI10.1017/S0962492906210018zbMath1185.65204WikidataQ56135370 ScholiaQ56135370MaRDI QIDQ3430639
Douglas N. Arnold, Ragnar Winther, Richard S. Falk
Publication date: 23 March 2007
Published in: Acta Numerica (Search for Journal in Brave)
Generalized finite element systems for smooth differential forms and Stokes' problem ⋮
Mixed finite elements for global tide models with nonlinear damping ⋮
Towards a unified analysis of mixed methods for elasticity with weakly symmetric stress ⋮
A family of mixed finite elements for the biharmonic equations on triangular and tetrahedral grids ⋮
Mixed finite elements for global tide models ⋮
\(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods ⋮
Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids ⋮
A new hierarchically-structured \(n\)-dimensional covariant form of rotating equations of geophysical fluid dynamics ⋮
Multigrid preconditioners for mixed finite element methods of the vector Laplacian ⋮
A new dual-mixed finite element method for the plane linear elasticity problem with pure traction boundary conditions ⋮
A superconvergent HDG method for Stokes flow with strongly enforced symmetry of the stress tensor ⋮
Residual-based a posteriori error estimation for multipoint flux mixed finite element methods ⋮
Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties ⋮
Stability of Lagrange elements for the mixed Laplacian ⋮
Arbitrary dimension convection-diffusion schemes for space-time discretizations ⋮
On optimal simplicial 3D meshes for minimizing the Hessian-based errors ⋮
Exact charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids: a geometric perspective ⋮
Bivariate spline differential forms ⋮
Construction of scalar and vector finite element families on polygonal and polyhedral meshes ⋮
Nodal finite element de Rham complexes ⋮
Stokes elements on cubic meshes yielding divergence-free approximations ⋮
A parameter-free stabilized finite element method for scalar advection-diffusion problems ⋮
\(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates ⋮
Spectral numerical exterior calculus methods for differential equations on radial manifolds ⋮
Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems ⋮
Characterization of the kernel of the operator CURL CURL ⋮
A discrete de Rham complex with enhanced smoothness ⋮
Variational discretization for rotating stratified fluids ⋮
Shape derivatives in differential forms. I: An intrinsic perspective ⋮
Symplectic-mixed finite element approximation of linear acoustic wave equations ⋮
Convergence of an adaptive mixed finite element method for convection-diffusion-reaction equations ⋮
Optimal second order rectangular elasticity elements with weakly symmetric stress ⋮
A Hamiltonian vorticity-dilatation formulation of the compressible Euler equations ⋮
Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation ⋮
Differential forms in lattice field theories: an overview ⋮
A new family of mixed methods for the Reissner-Mindlin plate model based on a system of first-order equations ⋮
Stokes, Maxwell and Darcy: a single finite element approximation for three model problems ⋮
Wave equation simulation on manifold by unconditional stable schemes ⋮
The discrete variational derivative method based on discrete differential forms ⋮
A fully discrete scheme for the pressure-stress formulation of the time-domain fluid-structure interaction problem ⋮
Convergence of a decoupled mixed FEM for the dynamic Ginzburg-Landau equations in nonsmooth domains with incompatible initial data ⋮
Two remarks on rectangular mixed finite elements for elasticity ⋮
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements ⋮
An arbitrary high-order spline finite element solver for the time domain Maxwell equations ⋮
A compatible high-order meshless method for the Stokes equations with applications to suspension flows ⋮
Structure-preserving discretization of incompressible fluids ⋮
Fast simplicial quadrature-based finite element operators using Bernstein polynomials ⋮
Orientational order on surfaces: the coupling of topology, geometry, and dynamics ⋮
Universal extension for Sobolev spaces of differential forms and applications ⋮
Formulation and computation of dynamic, interface-compatible Whitney complexes in three dimensions ⋮
Hp-finite element simulation of three-dimensional eddy current problems on multiply connected domains ⋮
A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations ⋮
Semilinear mixed problems on Hilbert complexes and their numerical approximation ⋮
Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces ⋮
Isogeometric analysis in electromagnetics: B-splines approximation ⋮
Geometric decompositions and local bases for spaces of finite element differential forms ⋮
Analysis of an augmented fully-mixed approach for the coupling of quasi-Newtonian fluids and porous media ⋮
A simple preconditioner for a discontinuous Galerkin method for the Stokes problem ⋮
New hybridized mixed methods for linear elasticity and optimal multilevel solvers ⋮
On the linearization of Regge calculus ⋮
Geometric, variational discretization of continuum theories ⋮
A new control volume finite element method for the stable and accurate solution of the drift-diffusion equations on general unstructured grids ⋮
Mixed \(hp\)-finite element method for linear elasticity with weakly imposed symmetry ⋮
Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions ⋮
An example of explicit implementation strategy and preconditioning for the high order edge finite elements applied to the time-harmonic Maxwell's equations ⋮
Computational bases for \(\mathcal {S}_{r}\Lambda^{1}(\mathbb {R}^{2})\) and their application in mixed finite element method ⋮
A posteriori error estimates for finite element exterior calculus: the de Rham complex ⋮
On the equivalence of the norms of the discrete differential forms in discrete exterior calculus ⋮
Handling the divergence constraints in Maxwell and Vlasov-Maxwell simulations ⋮
A residual-based a posteriori error estimator for the plane linear elasticity problem with pure traction boundary conditions ⋮
Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM ⋮
Difference forms ⋮
High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality ⋮
Hilbert complexes of nonlinear elasticity ⋮
Dual mixed finite element methods for the elasticity problem with Lagrange multipliers ⋮
The weak compatibility equations of nonlinear elasticity and the insufficiency of the Hadamard jump condition for non-simply connected bodies ⋮
Stable finite element methods preserving \(\nabla \cdot \boldsymbol{B}=0\) exactly for MHD models ⋮
Simplicial finite elements in higher dimensions. ⋮
Stable multilevel splittings of boundary edge element spaces ⋮
Discrete Lie advection of differential forms ⋮
Fully discrete semi-Lagrangian methods for advection of differential forms ⋮
A locking-free \(hp\) DPG method for linear elasticity with symmetric stresses ⋮
On Bogovskiĭ and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains ⋮
Hodge decompositions with mixed boundary conditions and applications to partial differential equations on Lipschitz manifolds ⋮
\texttt{FEMPAR}: an object-oriented parallel finite element framework ⋮
Analysis of linearized Galerkin-mixed FEMs for the time-dependent Ginzburg-Landau equations of superconductivity ⋮
Multiscale mixed finite elements ⋮
Optimization-based remap and transport: a divide and conquer strategy for feature-preserving discretizations ⋮
Mimetic finite difference method ⋮
Mimetic scalar products of discrete differential forms ⋮
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations ⋮
The chain collocation method: a spectrally accurate calculus of forms ⋮
Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms ⋮
High order geometric methods with exact conservation properties ⋮
A finite element exterior calculus framework for the rotating shallow-water equations ⋮
Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes ⋮
Locking-free Reissner-Mindlin elements without reduced integration ⋮
Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: a generalized moving least-squares (GMLS) approach ⋮
Mini-workshop: Mathematical and numerical analysis of Maxwell's equations. Abstracts from the mini-workshop held December 16--22, 2018 ⋮
Stabilized Galerkin for transient advection of differential forms
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