Convergence analysis of an adaptive edge element method for Maxwell's equations
From MaRDI portal
Publication:731961
DOI10.1016/j.apnum.2009.07.003zbMath1183.78032OpenAlexW2044100074MaRDI QIDQ731961
Jun Zou, Yifeng Xu, Junqing Chen
Publication date: 9 October 2009
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2009.07.003
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
RESIDUAL-BASED A POSTERIORI ESTIMATORS FOR THE A - φ MAGNETODYNAMIC HARMONIC FORMULATION OF THE MAXWELL SYSTEM ⋮ An adaptive edge element method and its convergence for a Saddle-Point problem from magnetostatics ⋮ A recovery-based a posteriori error estimator for \(H\)(curl) interface problems ⋮ A posteriori error analysis for the conical diffraction problem ⋮ A posteriori error estimator for mixed interior penalty discontinuous Galerkin finite element method for the \(\boldsymbol{H}(\operatorname{curl})\)-elliptic problems ⋮ Residual-based a posteriori estimators for the potential formulations of electrostatic and time-harmonic eddy current problems with voltage or current excitation ⋮ Convergence of Adaptive Mixed Finite Element Methods for the Hodge Laplacian Equation: Without Harmonic Forms ⋮ A residual-based a posteriori error estimator for the \(hp\)-finite element method for Maxwell's equations ⋮ An adaptive edge finite element method for electromagnetic cloaking simulation ⋮ A priori and posteriori error analysis for time-dependent Maxwell's equations ⋮ Adaptive Edge Element Approximation for H(curl) Elliptic Variational Inequalities of Second Kind ⋮ A lattice Boltzmann model for Maxwell's equations ⋮ Simulations of the rectangular wave-guide pattern in the complex Maxwell vorticity equations by lattice Boltzmann method ⋮ Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system ⋮ Convergence of an AEFEM for time-harmonic Maxwell equations with variable coefficients ⋮ Robust a posteriori error estimation for finite element approximation to \(\boldsymbol{H}(\mathbf{curl})\) problem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
- Mixed finite elements in \(\mathbb{R}^3\)
- Fully discrete finite element approaches for time-dependent Maxwell's equations
- A posteriori error indicators for Maxwell's equations
- Overlapping Schwarz methods for Maxwell's equations in three dimensions
- A posteriori error estimates for nonconforming finite element methods
- Adaptive finite element methods with convergence rates
- Optimality of a standard adaptive finite element method
- Convergence analysis of an adaptive nonconforming finite element method
- Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\)
- An adaptive finite element method for the H-\(\psi\) formulation of time-dependent eddy current problems
- A posteriori error estimation for the heterogeneous Maxwell equations on isotropic and anisotropic meshes
- Finite elements in computational electromagnetism
- Energy norm a posteriori error estimates for mixed finite element methods
- Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations
- Linear Convergence of an Adaptive Finite Element Method for the p-Laplacian Equation
- Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
- Finite Element Methods for Navier-Stokes Equations
- L2-Theory of the Maxwell operator in arbitrary domains
- Singularities of Maxwell interface problems
- Error Estimates for Adaptive Finite Element Computations
- Multigrid Method for Maxwell's Equations
- A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements
- A Nonoverlapping Domain Decomposition Method for Maxwell's Equations in Three Dimensions
- Data Oscillation and Convergence of Adaptive FEM
- Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations
- On the Efficiency of Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
- Convergence of Adaptive Finite Element Methods
- Finite Element Methods for Maxwell's Equations
- Overlapping Schwarz methods in H(curl) on polyhedral domains
- A posteriori error estimators for nonconforming finite element methods
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Residual based a posteriori error estimators for eddy current computation
- A Posteriori Error Estimators for the Raviart–Thomas Element
- An Adaptive Multilevel Method for Time‐Harmonic Maxwell Equations with Singularities
- A posteriori error estimates for Maxwell equations
- Error reduction and convergence for an adaptive mixed finite element method
- Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
- Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation
- A posteriori error estimators for elliptic equations with discontinuous coefficients
