Mixed finite elements in ?3

1980/09/01 by J. C. Nedelec, Jean-Claude Nédélec · 60 citations
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #Advanced Mathematical Modeling in Engineering

paper · doi:10.1007/bf01396415

Citations

• Les Inequations en Mecanique et en Physique

Cited by

• Optimal Finite-Element Interpolation on Curved Domains
• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries
• Two Complementary Approaches to Determine the Effective Index of Dielectric Ring Resonators
• A Lowest-Order Robust Mixed Finite Element Method with a Third-Order Tensor Variable for Strain Gradient Elasticity
• A family of mixed-mixed strongly conservative finite element methods for Biot's model of consolidation
• Global and local helicity-preservation in the finite element discretization of magnetic relaxation
• Discrete Compactness for p-Version of Tetrahedral Edge Elements
• Explicit implementation strategy of high order edge finite elements and Schwarz preconditioning for the time-harmonic Maxwell's equations
• The Basics of Weak Galerkin Finite Element Methods
• Continuous Finite Element Method For Maxwell Eigenvalue Problems With Regular Decomposition Technique
• Solving Two Dimensional H(curl)-elliptic Interface Systems with Optimal Convergence On Unfitted Meshes
• The Lebesgue constant for uniform approximation of differential forms
• A unified error analysis of HDG methods for the static Maxwell equations
• A structure-preserving semi-implicit four-split scheme for continuum mechanics
• Broken-FEEC on multipatch domains with local refinements
• SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus
• De Rham diagram for hp finite element spaces
• Formulae and transformations for simplicial tensorial finite elements via polytopal templates
• Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions
• General polytopal H(div) conformal finite elements and their\n discretisation spaces
• An exterior calculus framework for polytopal methods
• Numerical analysis for the nonlinear reduced-dimensional fracture model with pressure-dependent aperture
• A hybridizable discontinuous Galerkin method for the quad-curl problem
• A data-driven multiscale scheme for anisotropic finite strain magneto-elasticity
• Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes
• Ghost stabilisation for cut finite element exterior calculus
• Superconvergent and Divergence-Free Finite Element Methods for Stokes Equation
• A Cubic Whitney and Further Developments in Geometric Discretisation
• Nodal auxiliary a posteriori error estimates
• A Consistent Discrete 3D Hodge-type Decomposition: implementation and practical evaluation
• Nonconforming finite element Stokes complexes in three dimensions
• Harmonic potentials in the de Rham complex
• An analysis of the practical DPG method
• Convergence of Lagrange finite elements for the Maxwell Eigenvalue Problem in 2D
• Superconvergent HDG methods for Maxwell's equations via the M-decomposition
• Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div)
• Conforming and discontinuous discretizations of non-isothermal Darcy-Forchheimer flows
• Numerical validation of an explicit P1 finite-element scheme for Maxwell's equations in a polygon with variable permittivity away from its boundary
• An Extended Galerkin Analysis for Elliptic Problems
• HDG and CG methods for the Indefinite Time-Harmonic Maxwell's Equations under minimal regularity
• A note on devising HDG+ projections on polyhedral elements
• A Novel Conversion Technique from Nodal to Edge Finite Element Data Structure for Electromagnetic Analysis
• H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions
• Finite element conformal complexes in three dimensions
• Fitted norm preconditioners for the Hodge Laplacian in mixed form
• A Two-Step Darwin Model Time Domain Formulation for Quasistatic Electromagnetic Field Calculations
• Differential complexes and numerical stability
• From Whitney Forms to Metamaterials: a Rigorous Homogenization Theory
• Conforming Finite Elements for H(sym Curl) and H(dev sym Curl)
• On the vector potential formulation with an energy-based hysteresis model and its numerical solution
• Auxiliary iterative schemes for the discrete operators on de Rham complex
• Solving discrete constrained problems on de Rham complex
• A Two-Level Preconditioned Helmholtz-Jacobi-Davidson Method for the Maxwell Eigenvalue Problem
• A 2-complex containing Sobolev spaces of matrix fields
• A quasi-interpolation operator yielding fully computable error bounds
• Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs
• Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media
• Multigrid in H(div) on Axisymmetric Domains