Weighted regularization of Maxwell equations in polyhedral domains. A rehabilitation of Nodal finite elements
From MaRDI portal
Publication:1864505
DOI10.1007/s002110100388zbMath1019.78009OpenAlexW2068798260MaRDI QIDQ1864505
Monique Dauge, Martin Costabel
Publication date: 18 March 2003
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s002110100388
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10)
Related Items (only showing first 100 items - show all)
Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations ⋮ Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field ⋮ Mixed finite element approximation of incompressible MHD problems based on weighted regularization ⋮ Finite Element Methods for Maxwell's Equations ⋮ Fully discrete potential-based finite element methods for a transient eddy current problem ⋮ Weighted edge finite element method for Maxwell's equations with strong singularity ⋮ The Shifted-Inverse Iteration Based on the Multigrid Discretizations for Eigenvalue Problems ⋮ The $hp$-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations ⋮ Two Variants of Stabilized Nodal-Based FEM for the Magnetic Induction Problem ⋮ The optimal convergence rate of a \(C^{1}\) finite element method for non-smooth domains ⋮ Error analysis of the second-order BDF finite element scheme for the thermally coupled incompressible magnetohydrodynamic system ⋮ A Multiscale Approach and a Hybrid FE-FDTD Algorithm for 3D Time-Dependent Maxwell's Equations in Composite Materials ⋮ Computing electromagnetic eigenmodes with continuous Galerkin approximations ⋮ A new approximation technique for div-curl systems ⋮ Nodal finite element de Rham complexes ⋮ Interior energy error estimates for the weak Galerkin finite element method ⋮ Stabilized nodal-based finite element methods for the magnetic induction problem ⋮ Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics ⋮ ERMES: a nodal-based finite element code for electromagnetic simulations in frequency domain ⋮ Regularity of solutions of elliptic problems with a curved fracture ⋮ Temporal convergence of extrapolated BDF-2 scheme for the Maxwell-Landau-Lifshitz equations ⋮ Convergence analysis of a fully discrete finite element method for thermally coupled incompressible MHD problems with temperature-dependent coefficients ⋮ Computation of Maxwell singular solution by nodal-continuous elements ⋮ Mixed finite elements for electromagnetic analysis ⋮ Helmholtz's decomposition for compressible flows and its application to computational aeroacoustics ⋮ A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows ⋮ Convergence of Krylov subspace solvers with Schwarz preconditioner for the exterior Maxwell problem ⋮ Error estimate FEM for the Nikol'skij-Lizorkin problem with degeneracy ⋮ Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics ⋮ Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton-Krylov-AMG ⋮ Nonconforming Maxwell eigensolvers ⋮ A mixed DG method for linearized incompressible magnetohydrodynamics ⋮ Unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections ⋮ Multigrid discretization and iterative algorithm for mixed variational formulation of the eigenvalue problem of electric field ⋮ Convergence analysis of Crank-Nicolson extrapolated fully discrete scheme for thermally coupled incompressible magnetohydrodynamic system ⋮ Stokes, Maxwell and Darcy: a single finite element approximation for three model problems ⋮ On the Maxwell-wave equation coupling problem and its explicit finite-element solution. ⋮ New numerical method for solving time-harmonic Maxwell equations with strong singularity ⋮ Analysis of a continuous finite element method for \(H(\mathrm{curl},\mathrm{div})\)-elliptic interface problem ⋮ Approximation of the thermally coupled MHD problem using a stabilized finite element method ⋮ A Mixed $H^1$-Conforming Finite Element Method for Solving Maxwell's Equations with Non-$H^1$ Solution ⋮ A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem ⋮ Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron. ⋮ Mixed finite elements for incompressible magneto-hydrodynamics. ⋮ Finite element analysis for the axisymmetric Laplace operator on polygonal domains ⋮ About the gauge conditions arising in finite element magnetostatic problems ⋮ Highly efficient calculation schemes of finite-element filter approach for the eigenvalue problem of electric field ⋮ A two-scale discretization scheme for mixed variational formulation of eigenvalue problems ⋮ \(C ^{0}\) elements for generalized indefinite Maxwell equations ⋮ Isogeometric analysis in electromagnetics: B-splines approximation ⋮ New Mixed Elements for Maxwell Equations ⋮ Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system ⋮ On the existence and uniqueness of \(R_v\)-generalized solution for Dirichlet problem with singularity on all boundary ⋮ A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics ⋮ Isogeometric Analysis of the Steady-State Incompressible MHD Equations ⋮ The reconstruction of a time-dependent source from a surface measurement for full Maxwell's equations by means of the potential field method ⋮ Continuous Galerkin methods for solving the time-dependent Maxwell equations in 3D geometries ⋮ A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem ⋮ Time-dependent Maxwell's equations with charges in singular geometries ⋮ Weighted regularization for composite materials in electromagnetism ⋮ An anisotropic finite element method on polyhedral domains: Interpolation error analysis ⋮ Higher‐order discontinuous Galerkin method for pyramidal elements using orthogonal bases ⋮ APPLICATION OF DISCONTINUOUS GALERKIN SPECTRAL METHOD ON HEXAHEDRAL ELEMENTS FOR AEROACOUSTIC ⋮ Boundary coefficient determination for an eddy current problem based on the potential field method ⋮ On the proper generalized decomposition applied to microwave processes involving multilayered components ⋮ Mixed Finite Element Method with Gauss's Law Enforced for the Maxwell Eigenproblem ⋮ A new and simple implementation of the element-local \(L^2\)-projected continuous finite element method ⋮ Electrowetting of a 3D drop: numerical modelling with electrostatic vector fields ⋮ An amplitude finite element formulation for electromagnetic radiation and scattering ⋮ Algebraic convergence for anisotropic edge elements in polyhedral domains ⋮ Hodge decomposition to solve singular static Maxwell's equations in a non-convex polygon ⋮ Solving Maxwell's equations in singular domains with a Nitsche type method ⋮ A domain decomposition method for the parallelization of a three-dimensional Maxwell solver based on a constrained formulation ⋮ Augmented formulations for solving Maxwell equations ⋮ A goal-oriented \(hp\)-adaptive finite element approach to radar scattering problems ⋮ Unnamed Item ⋮ Approximation of PDE eigenvalue problems involving parameter dependent matrices ⋮ A stochastic approach to uncertainty in the equations of MHD kinematics ⋮ A Finite Element Method for a Curlcurl-Graddiv Eigenvalue Interface Problem ⋮ A mixed method for Maxwell eigenproblem ⋮ A convergent finite element method for the compressible magnetohydrodynamics system ⋮ Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM ⋮ A Convergent Linearized Lagrange Finite Element Method for the Magneto-hydrodynamic Equations in Two-Dimensional Nonsmooth and Nonconvex Domains ⋮ Singularities of eddy current problems ⋮ Error estimate of a fully discrete finite element method for incompressible vector potential magnetohydrodynamic system ⋮ A NONCONFORMING PENALTY METHOD FOR A TWO-DIMENSIONAL CURL–CURL PROBLEM ⋮ Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements ⋮ Highly efficient and energy stable schemes for the 2D/3D diffuse interface model of two-phase magnetohydrodynamics ⋮ The application of the \(hp\)-finite element method to electromagnetic problems ⋮ An Interior Penalty Method with C0Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity ⋮ NUMERICAL ANALYSIS OF THE GENERALIZED MAXWELL EQUATIONS (WITH AN ELLIPTIC CORRECTION) FOR CHARGED PARTICLE SIMULATIONS ⋮ Weighted Sobolev spaces and regularity for polyhedral domains ⋮ Approximation of eigenvalues in mixed form, discrete compactness property, and application to \(hp\) mixed finite elements ⋮ Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements ⋮ A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations ⋮ Discontinuous least-squares finite element method for the div-curl problem ⋮ A stabilized \(P1\) domain decomposition finite element method for time harmonic Maxwell's equations ⋮ SOLVING NUMERICALLY THE STATIC MAXWELL EQUATIONS IN AN AXISYMMETRIC SINGULAR GEOMETRY ⋮ Analysis of a new mixed FEM for stationary incompressible magneto-hydrodynamics ⋮ Stabilized interior penalty methods for the time-harmonic Maxwell equations.
This page was built for publication: Weighted regularization of Maxwell equations in polyhedral domains. A rehabilitation of Nodal finite elements
