A virtual finite element method for two-dimensional Maxwell interface problems with a background unfitted mesh
From MaRDI portal
Publication:5024419
DOI10.1142/S0218202521500652zbMath1478.65117arXiv2103.04582OpenAlexW3208463764MaRDI QIDQ5024419
Ruchi Guo, Shuhao Cao, Long Chen
Publication date: 31 January 2022
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.04582
virtual elementsanisotropic error analysis\( \boldsymbol{H}(\text{curl})\)-elliptic equationsMaxwell interface problems
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items (13)
Interpolation and stability estimates for edge and face virtual elements of general order ⋮ An immersed Raviart-Thomas mixed finite element method for elliptic interface problems on unfitted meshes ⋮ Immersed virtual element methods for elliptic interface problems in two dimensions ⋮ A reconstructed discontinuous approximation on unfitted meshes to \(H(\mathrm{curl})\) and \(H(\mathrm{div})\) interface problems ⋮ Immersed virtual element methods for electromagnetic interface problems in three dimensions ⋮ A conforming virtual element method based on unfitted meshes for the elliptic interface problem ⋮ High-order weak Galerkin scheme for \(\mathbf{H} (\mathrm{div})\)-elliptic interface problems ⋮ A nonconforming immersed virtual element method for elliptic interface problems ⋮ The virtual element method for the 3D resistive magnetohydrodynamic model ⋮ A Family of Immersed Finite Element Spaces and Applications to Three-Dimensional \(\bf{H}(\operatorname{curl})\) Interface Problems ⋮ Virtual element method for control constrained Dirichlet boundary control problem governed by the diffusion problem ⋮ A \(C^1\)-\(C^0\) virtual element discretization for a sixth-order elliptic equation ⋮ Recent results and perspectives for virtual element methods
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
- An adaptive FEM for a Maxwell interface problem
- Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation
- An optimal Poincaré inequality for convex domains
- The adaptive immersed interface finite element method for elliptic and Maxwell interface problems
- A weak Galerkin finite element method for the Maxwell equations
- Optimal a priori estimates for higher order finite elements for elliptic interface problems
- Mixed finite elements in \(\mathbb{R}^3\)
- Fully discrete finite element approaches for time-dependent Maxwell's equations
- An interface-fitted mesh generator and virtual element methods for elliptic interface problems
- Interior penalty method for the indefinite time-harmonic Maxwell equations
- High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
- Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems
- A simple virtual element-based flux recovery on quadtree
- Interface-penalty finite element methods for interface problems in \(H^1\), \(\boldsymbol{H} (\mathbf{curl})\), and \(\boldsymbol{H} (\operatorname{div})\)
- Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains
- Virtual element approximation of 2D magnetostatic problems
- Algebraic convergence for anisotropic edge elements in polyhedral domains
- A recovery-based a posteriori error estimator for \(H\)(curl) interface problems
- Uniform a priori estimates for elliptic and static Maxwell interface problems
- CutFEM: Discretizing geometry and partial differential equations
- Finite elements in computational electromagnetism
- A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations
- A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
- An Inexpensive Method for the Evaluation of the Solution of the Lowest Order Raviart–Thomas Mixed Method
- Singularities of Maxwell interface problems
- Analysis of a Finite Element Method for Maxwell’s Equations
- On the Maximum Angle Condition for Linear Tetrahedral Elements
- On the Angle Condition in the Finite Element Method
- The Maximum Angle Condition for Mixed and Nonconforming Elements: Application to the Stokes Equations
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- A Justification of Eddy Currents Model for the Maxwell Equations
- Finite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients
- DG Treatment of Non-conforming Interfaces in 3D Curl-Curl Problems
- Mixed Discontinuous Galerkin Approximation of the Maxwell Operator
- Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes
- Mixed formulations for finite element analysis of magnetostatic and electrostatic problems
- Finite Element Methods for Maxwell's Equations
- Analysis of finite element approximation for time-dependent Maxwell problems
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- Residual based a posteriori error estimators for eddy current computation
- A group of immersed finite-element spaces for elliptic interface problems
This page was built for publication: A virtual finite element method for two-dimensional Maxwell interface problems with a background unfitted mesh
