A new primal-dual weak Galerkin method for elliptic interface problems with low regularity assumptions

DOI10.1016/j.jcp.2022.111538OpenAlexW3096329550WikidataQ114666187 ScholiaQ114666187MaRDI QIDQ2083621

Chunmei Wang, Junping Wang, Waixiang Cao

Publication date: 11 October 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.14564

zbMATH Keywords

finite element methodslow regularityelliptic interface problemsprimal-dual weak GalerkinPDWGpolygonal or polyhedral partition

Mathematics Subject Classification ID

Numerical methods for partial differential equations, boundary value problems (65Nxx) Miscellaneous topics in partial differential equations (35Rxx) Elliptic equations and elliptic systems (35Jxx)

Related Items (4)

Optimal a priori error estimates for elliptic interface problems: weak Galerkin mixed finite element approximations ⋮ High-order weak Galerkin scheme for \(\mathbf{H} (\mathrm{div})\)-elliptic interface problems ⋮ Curved elements in weak Galerkin finite element methods ⋮ Generalized weak Galerkin finite element methods for biharmonic equations

Uses Software

• MIBPB
• IIMPACK

Cites Work

• Unnamed Item
• MIBPB
• Weak Galerkin methods for second order elliptic interface problems
• A kernel-free boundary integral method for implicitly defined surfaces
• Using integral equations and the immersed interface method to solve immersed boundary problems with stiff forces
• A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions
• A weak formulation for solving elliptic interface problems without body fitted grid
• A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions
• Finite element approximation of the Navier-Stokes equations
• Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient
• A finite element method for interface problems in domains with smooth boundaries and interfaces
• A numerical method for solving variable coefficient elliptic equation with interfaces
• A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces
• Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
• Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
• High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces
• Analysis of an efficient finite element method for embedded interface problems
• A second order virtual node method for elliptic problems with interfaces and irregular domains
• On computational issues of immersed finite element methods
• A three-dimensional computational method for blood flow in the heart. I: Immersed elastic fibers in a viscous incompressible fluid
• Numerical analysis of blood flow in the heart
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• The immersed finite volume element methods for the elliptic interface problems
• A hybrid method for moving interface problems with application to the Hele-Shaw flow
• Finite element methods and their convergence for elliptic and parabolic interface problems
• A new weak Galerkin finite element method for elliptic interface problems
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
• A fictitious domain method for Dirichlet problem and applications
• Primal-dual weak Galerkin finite element methods for elliptic Cauchy problems
• Solving elliptic interface problems with jump conditions on Cartesian grids
• MIB Galerkin method for elliptic interface problems
• A coupling interface method for elliptic interface problems
• A Galerkin formulation of the MIB method for three dimensional elliptic interface problems
• Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
• BDDC methods for discontinuous Galerkin discretization of elliptic problems
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
• Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
• A high-order hybridizable discontinuous Galerkin method for elliptic interface problems
• A discontinuous Galerkin method for elliptic interface problems with application to electroporation
• A weak Galerkin mixed finite element method for second order elliptic problems
• Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems
• Convergence analysis of theQ₁-finite element method for elliptic problems with non-boundary-fitted meshes
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
• The Immersed Interface Method

This page was built for publication: A new primal-dual weak Galerkin method for elliptic interface problems with low regularity assumptions