Convergence analysis of finite element methods for H(div;Ω)-elliptic interface problems

DOI10.1515/JNUM.2010.010zbMath1203.65227OpenAlexW2079823607MaRDI QIDQ3056346

Jingzhi Li, Jun Zou, Ralf Hiptmair

Publication date: 12 November 2010

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jnum.2010.010

zbMATH Keywords

triangulationconvergencenumerical examplesfinite element methodsface elementstetrahedral meshesoptimal error estimateelliptic interface problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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 (20)

An extended mixed finite element method for elliptic interface problems ⋮ Weak Galerkin methods for second order elliptic interface problems ⋮ A Galerkin formulation of the MIB method for three dimensional elliptic interface problems ⋮ A new weak Galerkin finite element method for elliptic interface problems ⋮ Interface-penalty finite element methods for interface problems in \(H^1\), \(\boldsymbol{H} (\mathbf{curl})\), and \(\boldsymbol{H} (\operatorname{div})\) ⋮ An extended finite element method for coupled Darcy–Stokes problems ⋮ 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 ⋮ Unfitted finite element methods for the heat conduction in composite media with contact resistance ⋮ High-order weak Galerkin scheme for \(\mathbf{H} (\mathrm{div})\)-elliptic interface problems ⋮ Analysis of a continuous finite element method for \(H(\mathrm{curl},\mathrm{div})\)-elliptic interface problem ⋮ A Family of Immersed Finite Element Spaces and Applications to Three-Dimensional \(\bf{H}(\operatorname{curl})\) Interface Problems ⋮ Weak Galerkin finite element methods with and without stabilizers for H(div;Ω)${\bf H}(\mbox{div}; \Omega )$‐elliptic problems ⋮ A high-order source removal finite element method for a class of elliptic interface problems ⋮ A hybrid finite difference/control volume method for the three dimensional poroelastic wave equations in the spherical coordinate system ⋮ MIB Galerkin method for elliptic interface problems ⋮ Unnamed Item ⋮ Augmented immersed finite element methods for some elliptic partial differential equations ⋮ A posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction ⋮ A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity

Cites Work

• A finite element method for interface problems in domains with smooth boundaries and interfaces
• A convergence theory of multilevel additive Schwarz methods on unstructured meshes
• Optimal a priori estimates for higher order finite elements for elliptic interface problems
• Mixed finite elements in \(\mathbb{R}^3\)
• Finite element methods and their convergence for elliptic and parabolic interface problems
• Optimal a priori estimates for interface problems
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Finite elements in computational electromagnetism
• Fitted and Unfitted Finite-Element Methods for Elliptic Equations with Smooth Interfaces
• First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
• Preconditioning in H(𝑑𝑖𝑣) and applications
• A Simple Mesh Generator in MATLAB
• A mortar element method for elliptic problems with discontinuous coefficients
• Preconditioning Mixed Finite Element Saddle-point Elliptic Problems
• Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces

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