A selective immersed discontinuous Galerkin method for elliptic interface problems
From MaRDI portal
Publication:5415921
DOI10.1002/mma.2856zbMath1292.65126OpenAlexW2168805210MaRDI QIDQ5415921
Tao Lin, Xiaoming He, Yan Ping Lin
Publication date: 19 May 2014
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mma.2856
numerical examplesmesh refinementpenaltysecond-order elliptic interface problemsimmersed finite elementsselective discontinuous Galerkin
Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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Cites Work
- Scalable Direct Vlasov Solver with Discontinuous Galerkin Method on Unstructured Mesh
- Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
- The Direct Discontinuous Galerkin (DDG) Method for Diffusion with Interface Corrections
- The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
- A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations
- A Parallel, Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids
- On the Connection Between the Spectral Difference Method and the Discontinuous Galerkin Method
- Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws
- The Immersed Interface Method
- Finite Element Methods and Their Applications
- A summary of numerical methods for time-dependent advection-dominated partial differential equations
- Modeling holes and inclusions by level sets in the extended finite element method
- On the coupling of local discontinuous Galerkin and conforming finite element methods
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
- A new high-order discontinuous Galerkin spectral finite element method for Lagrangian gas dynamics in two-dimensions
- Immersed finite element methods for 4th order differential equations
- High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
- Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field
- Block preconditioners for LDG discretizations of linear incompressible flow problems
- Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient
- On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
- A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations
- A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows
- Space-time discontinuous Galerkin finite element method for two-fluid flows
- A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems
- A central discontinuous Galerkin method for Hamilton-Jacobi equations
- Analysis of space-time discontinuous Galerkin method for nonlinear convection-diffusion problems
- A discontinuous Galerkin method combined with mixed finite element for seawater intrusion problem
- On the coupling of finite volume and discontinuous Galerkin method for elliptic problems
- A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: the hyperbolic operator
- An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations
- Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms
- Discontinuous Galerkin spectral element approximations on moving meshes
- A class of domain decomposition preconditioners for \(hp\)-discontinuous Galerkin finite element methods
- Discontinuous Galerkin methods for second-order elliptic PDE with low-regularity solutions
- A finite element method for interface problems in domains with smooth boundaries and interfaces
- A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions
- Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
- Composite finite elements for elliptic boundary value problems with discontinuous coefficients
- Local discontinuous Galerkin methods for the generalized Zakharov system
- On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
- Optimal convergence analysis of an immersed interface finite element method
- A \(p\)-th degree immersed finite element for boundary value problems with discontinuous coefficients
- An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations
- Finite difference methods on irregular networks. A generalized approach to second order elliptic problems. (Licensed ed.)
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- Numerical analysis of blood flow in the heart
- Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers
- A discontinuous \(hp\) finite element method for diffusion problems
- The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
- The immersed interface method using a finite element formulation
- The immersed finite volume element methods for the elliptic interface problems
- The embedded curved boundary method for orthogonal simulation meshes
- Finite element methods and their convergence for elliptic and parabolic interface problems
- New Cartesian grid methods for interface problems using the finite element formulation
- Developments in Cartesian cut cell methods
- Asymptotic boundary conditions with immersed finite elements for interface magnetostatic/electrostatic field problems with open boundary
- On the local discontinuous Galerkin method for linear elasticity
- A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis
- Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
- Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems
- High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
- Quadratic immersed finite element spaces and their approximation capabilities
- The finite element method for elliptic equations with discontinuous coefficients
- Flow patterns around heart valves: A numerical method
- Arbitrary discontinuities in finite elements
- A Trilinear Immersed Finite Element Method for Solving the Electroencephalography Forward Problem
- Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems
- An Analysis of a Broken $P_1$-Nonconforming Finite Element Method for Interface Problems
- Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
- Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions
- On the Poincaré-Friedrichs inequality for piecewise $H^\{1\}$ functions in anisotropic discontinuous Galerkin finite element methods
- Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
- A Posteriori Error Control for Discontinuous Galerkin Methods for Parabolic Problems
- Refinement and Connectivity Algorithms for Adaptive Discontinuous Galerkin Methods
- Simplified immersed interface methods for elliptic interface problems with straight interfaces
- The convergence of the bilinear and linear immersed finite element solutions to interface problems
- Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- An efficient second-order accurate cut-cell method for solving the variable coefficient Poisson equation with jump conditions on irregular domains
- Three-dimensional immersed finite element methods for electric field simulation in composite materials
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- L2stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
- Approximation capability of a bilinear immersed finite element space
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- Uniform superconvergence analysis of the discontinuous Galerkin method for a singularly perturbed problem in 1-D
- Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
- Coupling Discontinuous Galerkin and Mixed Finite Element Discretizations using Mortar Finite Elements
- An Implicit Matching Principle for Global Element Calculations
- 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
- Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- THE PARTITION OF UNITY METHOD
- A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
- Numerical study of theHP version of mixed discontinuous finite element methods for reaction-diffusion problems: The 1D case
- Stability and convergence of mixed discontinuous finite element methods for second-order differential problems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- An immersed finite element space and its approximation capability
- Eulerian-Lagrangian localized adjoint methods for convection-diffusion equations and their convergence analysis
- Immersed finite element methods for parabolic equations with moving interface
- A finite element method for crack growth without remeshing
- Can a finite element method perform arbitrarily badly?
