High order symmetric direct discontinuous Galerkin method for elliptic interface problems with fitted mesh

DOI10.1016/j.jcp.2020.109301zbMath1435.65204OpenAlexW3006047440MaRDI QIDQ778266

Hongying Huang, Jue Yan, Jin Li

Publication date: 2 July 2020

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2020.109301

zbMATH Keywords

direct discontinuous Galerkin methodelliptic interface problem

Mathematics Subject Classification ID

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

A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions, Superconvergence study of the direct discontinuous Galerkin method and its variations for diffusion equations, A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations, A generalized framework for direct discontinuous Galerkin methods for nonlinear diffusion equations, A high order discontinuous Galerkin method for the recovery of the conductivity in electrical impedance tomography, Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements

Cites Work

• Unnamed Item
• Unnamed Item
• Weak Galerkin methods for second order elliptic interface problems
• Direct discontinuous Galerkin method and its variations for second order elliptic equations
• Fictitious domain finite element methods using cut elements. I: A stabilized Lagrange multiplier method
• A curved boundary treatment for discontinuous Galerkin schemes solving time dependent problems
• Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes
• On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
• Numerical analysis of blood flow in the heart
• The immersed interface method using a finite element formulation
• Finite element methods and their convergence for elliptic and parabolic interface problems
• The direct coupling of local discontinuous Galerkin and natural boundary element method for nonlinear interface problem in \(\mathbb{R}^3\)
• Fourier type super convergence study on DDGIC and symmetric DDG methods
• An unfitted interface penalty finite element method for elliptic interface problems
• Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
• Higher-order finite element methods for elliptic problems with interfaces
• Adaptive Mesh Refinement and Superconvergence for Two-Dimensional Interface Problems
• A new multiscale finite element method for high-contrast elliptic interface problems
• A Triangulation Algorithm for Fast Elliptic Solvers Based on Domain Imbedding
• The immersed boundary method
• On the coupling of local discontinuous Galerkin and boundary element methods for non-linear exterior transmission problems
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
• High degree efficient symmetrical Gaussian quadrature rules for the triangle
• An Interior Penalty Finite Element Method with Discontinuous Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• An Immersed Interface Method for Incompressible Navier--Stokes Equations
• A Local Discontinuous Galerkin Method for Nonlinear Diffusion Problems with Mixed Boundary Conditions
• An immersed finite element space and its approximation capability
• A New Direct Discontinuous Galerkin Method with Symmetric Structure for Nonlinear Diffusion Equations
• Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
• The Direct Discontinuous Galerkin (DDG) Method for Diffusion with Interface Corrections
• The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems