A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes

Mu, Lin

doi:10.1016/j.cam.2018.09.007

Title: A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes

Authors:

Publication Date:: 2019-12-01

Sponsoring Org.:: USDOE

OSTI Identifier:: 1636506

Grant/Contract Number:: ERKJ259; ERKJ320; AC05-00OR22725

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Journal of Computational and Applied Mathematics

Additional Journal Information:: Journal Name: Journal of Computational and Applied Mathematics Journal Volume: 362 Journal Issue: C; Journal ID: ISSN 0377-0427

Publisher:: Elsevier

Country of Publication:: Belgium

Language:: English

Citation Formats


                    Mu, Lin. A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes.  Belgium: N. p., 2019. 
Web.  doi:10.1016/j.cam.2018.09.007.

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                    Mu, Lin. A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes.  Belgium.  https://doi.org/10.1016/j.cam.2018.09.007

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                    Mu, Lin. Sun .  
"A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes".  Belgium.  https://doi.org/10.1016/j.cam.2018.09.007.

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@article{osti_1636506,

  title        = {A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes},

  author       = {Mu, Lin},

  abstractNote = {},

  doi          = {10.1016/j.cam.2018.09.007},

  journal      = {Journal of Computational and Applied Mathematics},

  number       = C,

  volume       = 362,

  place        = {Belgium},

  year         = {2019},

  month        = {12}

}

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https://doi.org/10.1016/j.cam.2018.09.007

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Title: A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes

Citation Formats

Topology optimization using polytopes journal, August 2015

An Interior Penalty Finite Element Method with Discontinuous Elements journal, August 1982

An Elliptic Collocation-Finite Element Method with Interior Penalties journal, February 1978

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems journal, January 2002

Discontinuous hp -Finite Element Methods for Advection-Diffusion-Reaction Problems journal, January 2002

A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems journal, May 2008

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems journal, January 2009

Basic Principles of Virtual Element Methods journal, November 2012

A virtual element method with arbitrary regularity journal, July 2013

Basic principles of mixed Virtual Element Methods journal, July 2014

Some basic formulations of the virtual element method (VEM) for finite deformations journal, May 2017

A hybrid mortar virtual element method for discrete fracture network simulations journal, February 2016

Virtual Element Method for general second-order elliptic problems on polygonal meshes journal, February 2016

Stability analysis for the virtual element method journal, October 2017

The NonConforming Virtual Element Method for the Stokes Equations journal, January 2016

A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem journal, April 2016

A weak Galerkin finite element method for second-order elliptic problems journal, March 2013

A weak Galerkin mixed finite element method for second order elliptic problems journal, May 2014

Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes journal, February 2014

Weak Galerkin finite element methods for Parabolic equations: Weak Galerkin Finite Element Method journal, May 2013

A Weak Galerkin Finite Element Method for the Maxwell Equations journal, December 2014

A weak Galerkin finite element method for the stokes equations journal, May 2015

A New Weak Galerkin Finite Element Scheme for the Brinkman Model journal, May 2016

A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation journal, December 2016

A weak Galerkin finite element scheme for solving the stationary Stokes equations journal, August 2016

A new weak Galerkin finite element method for the Helmholtz equation journal, June 2014

A new weak Galerkin finite element method for elliptic interface problems journal, November 2016

Design and data structure of fully adaptive, multigrid, finite-element software journal, August 1984

Mesh Refinement Processes Based on the Generalized Bisection of Simplices journal, June 1984

Convergence analysis of the high-order mimetic finite difference method journal, May 2009

A Virtual Element Method for elastic and inelastic problems on polytope meshes journal, October 2015

Mixed virtual element methods for general second order elliptic problems on polygonal meshes journal, May 2016

The arbitrary order mixed mimetic finite difference method for the diffusion equation journal, May 2016

Hybrid high-order methods for variable-diffusion problems on general meshes journal, January 2015

A hybrid high-order locking-free method for linear elasticity on general meshes journal, January 2015

A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes journal, January 2015

Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes journal, May 2016

PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab journal, January 2012

A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-linear Elliptic Problems journal, October 2012

Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations journal, January 2011

A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems journal, August 2013

A-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems journal, May 2009

A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media journal, November 2014

A posteriori error estimates for discontinuous Galerkin methods of obstacle problems journal, April 2015

On recursive refinement of convex polygons journal, July 2016

On the poisson equation with intersecting interfaces journal, January 1974

Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM journal, January 2017

Topology optimization using polytopes
journal, August 2015

An Interior Penalty Finite Element Method with Discontinuous Elements
journal, August 1982

An Elliptic Collocation-Finite Element Method with Interior Penalties
journal, February 1978

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
journal, January 2002

Discontinuous hp -Finite Element Methods for Advection-Diffusion-Reaction Problems
journal, January 2002

A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
journal, May 2008

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
journal, January 2009

Basic Principles of Virtual Element Methods
journal, November 2012

A virtual element method with arbitrary regularity
journal, July 2013

Basic principles of mixed Virtual Element Methods
journal, July 2014

Some basic formulations of the virtual element method (VEM) for finite deformations
journal, May 2017

A hybrid mortar virtual element method for discrete fracture network simulations
journal, February 2016

Virtual Element Method for general second-order elliptic problems on polygonal meshes
journal, February 2016

Stability analysis for the virtual element method
journal, October 2017

The NonConforming Virtual Element Method for the Stokes Equations
journal, January 2016

A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem
journal, April 2016

A weak Galerkin finite element method for second-order elliptic problems
journal, March 2013

A weak Galerkin mixed finite element method for second order elliptic problems
journal, May 2014

Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
journal, February 2014

Weak Galerkin finite element methods for Parabolic equations: Weak Galerkin Finite Element Method
journal, May 2013

A Weak Galerkin Finite Element Method for the Maxwell Equations
journal, December 2014

A weak Galerkin finite element method for the stokes equations
journal, May 2015

A New Weak Galerkin Finite Element Scheme for the Brinkman Model
journal, May 2016

A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation
journal, December 2016

A weak Galerkin finite element scheme for solving the stationary Stokes equations
journal, August 2016

A new weak Galerkin finite element method for the Helmholtz equation
journal, June 2014

A new weak Galerkin finite element method for elliptic interface problems
journal, November 2016

Design and data structure of fully adaptive, multigrid, finite-element software
journal, August 1984

Mesh Refinement Processes Based on the Generalized Bisection of Simplices
journal, June 1984

Convergence analysis of the high-order mimetic finite difference method
journal, May 2009

A Virtual Element Method for elastic and inelastic problems on polytope meshes
journal, October 2015

Mixed virtual element methods for general second order elliptic problems on polygonal meshes
journal, May 2016

The arbitrary order mixed mimetic finite difference method for the diffusion equation
journal, May 2016

Hybrid high-order methods for variable-diffusion problems on general meshes
journal, January 2015

A hybrid high-order locking-free method for linear elasticity on general meshes
journal, January 2015

A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes
journal, January 2015

Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes
journal, May 2016

PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab
journal, January 2012

A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-linear Elliptic Problems
journal, October 2012

Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations
journal, January 2011

A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems
journal, August 2013

A-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems
journal, May 2009

A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
journal, November 2014

A posteriori error estimates for discontinuous Galerkin methods of obstacle problems
journal, April 2015

On recursive refinement of convex polygons
journal, July 2016

On the poisson equation with intersecting interfaces
journal, January 1974

Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM
journal, January 2017