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

Journal Article · 01 December 2019 · Journal of Computational and Applied Mathematics

DOI: https://doi.org/10.1016/j.cam.2018.09.007 · OSTI ID:2242528

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Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2242528

Journal Information:: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: C Vol. 362; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: Belgium

Language:: English

References (45)

Weak Galerkin finite element methods for Parabolic equations: Weak Galerkin Finite Element Method Li, Qiaoluan H.; Wang, Junping Numerical Methods for Partial Differential Equations, Vol. 29, Issue 6 https://doi.org/10.1002/num.21786	journal	May 2013
Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes Mu, Lin; Wang, Junping; Ye, Xiu Numerical Methods for Partial Differential Equations, Vol. 30, Issue 3 https://doi.org/10.1002/num.21855	journal	February 2014
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab Talischi, Cameron; Paulino, Glaucio H.; Pereira, Anderson Structural and Multidisciplinary Optimization, Vol. 45, Issue 3 https://doi.org/10.1007/s00158-011-0706-z	journal	January 2012
Convergence analysis of the high-order mimetic finite difference method Beirão da Veiga, L.; Lipnikov, K.; Manzini, G. Numerische Mathematik, Vol. 113, Issue 3 https://doi.org/10.1007/s00211-009-0234-6	journal	May 2009
A weak Galerkin finite element method for the stokes equations Wang, Junping; Ye, Xiu Advances in Computational Mathematics, Vol. 42, Issue 1 https://doi.org/10.1007/s10444-015-9415-2	journal	May 2015
A-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems Lovadina, Carlo; Marini, L. Donatella Journal of Scientific Computing, Vol. 40, Issue 1-3 https://doi.org/10.1007/s10915-009-9286-0	journal	May 2009
A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-linear Elliptic Problems Bi, Chunjia; Ginting, Victor Journal of Scientific Computing, Vol. 55, Issue 3 https://doi.org/10.1007/s10915-012-9651-2	journal	October 2012
A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems Chen, Long; Wang, Junping; Ye, Xiu Journal of Scientific Computing, Vol. 59, Issue 2 https://doi.org/10.1007/s10915-013-9771-3	journal	August 2013
A Weak Galerkin Finite Element Method for the Maxwell Equations Mu, Lin; Wang, Junping; Ye, Xiu Journal of Scientific Computing, Vol. 65, Issue 1 https://doi.org/10.1007/s10915-014-9964-4	journal	December 2014
On recursive refinement of convex polygons Lai, Ming-Jun; Slavov, George Computer Aided Geometric Design, Vol. 45 https://doi.org/10.1016/j.cagd.2016.04.002	journal	July 2016
A weak Galerkin finite element method for second-order elliptic problems Wang, Junping; Ye, Xiu Journal of Computational and Applied Mathematics, Vol. 241 https://doi.org/10.1016/j.cam.2012.10.003	journal	March 2013
A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation Wang, Chunmei; Wang, Junping; Wang, Ruishu Journal of Computational and Applied Mathematics, Vol. 307 https://doi.org/10.1016/j.cam.2015.12.015	journal	December 2016
A weak Galerkin finite element scheme for solving the stationary Stokes equations Wang, Ruishu; Wang, Xiaoshen; Zhai, Qilong Journal of Computational and Applied Mathematics, Vol. 302 https://doi.org/10.1016/j.cam.2016.01.025	journal	August 2016
Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM Weißer, Steffen Computers & Mathematics with Applications, Vol. 73, Issue 2 https://doi.org/10.1016/j.camwa.2016.11.013	journal	January 2017
A hybrid high-order locking-free method for linear elasticity on general meshes Di Pietro, Daniele A.; Ern, Alexandre Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.09.009	journal	January 2015
Topology optimization using polytopes Gain, Arun L.; Paulino, Glaucio H.; Duarte, Leonardo S. Computer Methods in Applied Mechanics and Engineering, Vol. 293 https://doi.org/10.1016/j.cma.2015.05.007	journal	August 2015
A Virtual Element Method for elastic and inelastic problems on polytope meshes Beirão da Veiga, L.; Lovadina, C.; Mora, D. Computer Methods in Applied Mechanics and Engineering, Vol. 295 https://doi.org/10.1016/j.cma.2015.07.013	journal	October 2015
Some basic formulations of the virtual element method (VEM) for finite deformations Chi, H.; da Veiga, L. Beirão; Paulino, G. H. Computer Methods in Applied Mechanics and Engineering, Vol. 318 https://doi.org/10.1016/j.cma.2016.12.020	journal	May 2017
Hybrid high-order methods for variable-diffusion problems on general meshes Di Pietro, Daniele A.; Ern, Alexandre Comptes Rendus Mathematique, Vol. 353, Issue 1 https://doi.org/10.1016/j.crma.2014.10.013	journal	January 2015
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media Di Pietro, Daniele A.; Flauraud, Eric; Vohralík, Martin Journal of Computational Physics, Vol. 276 https://doi.org/10.1016/j.jcp.2014.06.061	journal	November 2014
A hybrid mortar virtual element method for discrete fracture network simulations Benedetto, Matías Fernando; Berrone, Stefano; Borio, Andrea Journal of Computational Physics, Vol. 306 https://doi.org/10.1016/j.jcp.2015.11.034	journal	February 2016
A new weak Galerkin finite element method for elliptic interface problems Mu, Lin; Wang, Junping; Ye, Xiu Journal of Computational Physics, Vol. 325 https://doi.org/10.1016/j.jcp.2016.08.024	journal	November 2016
A posteriori error estimates for discontinuous Galerkin methods of obstacle problems Wang, Fei; Han, Weimin; Eichholz, Joseph Nonlinear Analysis: Real World Applications, Vol. 22 https://doi.org/10.1016/j.nonrwa.2014.08.011	journal	April 2015
Mixed virtual element methods for general second order elliptic problems on polygonal meshes Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, Luisa Donatella ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 50, Issue 3 https://doi.org/10.1051/m2an/2015067	journal	May 2016
The arbitrary order mixed mimetic finite difference method for the diffusion equation Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 50, Issue 3 https://doi.org/10.1051/m2an/2015088	journal	May 2016
On the poisson equation with intersecting interfaces Bruce kellogg, R. Applicable Analysis, Vol. 4, Issue 2 https://doi.org/10.1080/00036817408839086	journal	January 1974
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny Mathematics of Computation, Vol. 77, Issue 264 https://doi.org/10.1090/S0025-5718-08-02123-6	journal	May 2008
A weak Galerkin mixed finite element method for second order elliptic problems Wang, Junping; Ye, Xiu Mathematics of Computation, Vol. 83, Issue 289 https://doi.org/10.1090/S0025-5718-2014-02852-4	journal	May 2014
A virtual element method with arbitrary regularity da Veiga, L. B.; Manzini, G. IMA Journal of Numerical Analysis, Vol. 34, Issue 2 https://doi.org/10.1093/imanum/drt018	journal	July 2013
A new weak Galerkin finite element method for the Helmholtz equation Mu, Lin; Wang, Junping; Ye, Xiu IMA Journal of Numerical Analysis, Vol. 35, Issue 3 https://doi.org/10.1093/imanum/dru026	journal	June 2014
A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem Cáceres, Ernesto; Gatica, Gabriel N. IMA Journal of Numerical Analysis, Vol. 37, Issue 1 https://doi.org/10.1093/imanum/drw002	journal	April 2016
Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes Di Pietro, Daniele A.; Ern, Alexandre IMA Journal of Numerical Analysis, Vol. 37, Issue 1 https://doi.org/10.1093/imanum/drw003	journal	May 2016
Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Lazarov, Raytcho SIAM Journal on Numerical Analysis, Vol. 47, Issue 2 https://doi.org/10.1137/070706616	journal	January 2009
An Elliptic Collocation-Finite Element Method with Interior Penalties Wheeler, Mary Fanett SIAM Journal on Numerical Analysis, Vol. 15, Issue 1 https://doi.org/10.1137/0715010	journal	February 1978
An Interior Penalty Finite Element Method with Discontinuous Elements Arnold, Douglas N. SIAM Journal on Numerical Analysis, Vol. 19, Issue 4 https://doi.org/10.1137/0719052	journal	August 1982
Mesh Refinement Processes Based on the Generalized Bisection of Simplices Rivara, Maria-Cecilia SIAM Journal on Numerical Analysis, Vol. 21, Issue 3 https://doi.org/10.1137/0721042	journal	June 1984
Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations Cai, Zhiqiang; Ye, Xiu; Zhang, Shun SIAM Journal on Numerical Analysis, Vol. 49, Issue 5 https://doi.org/10.1137/100805133	journal	January 2011
A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes Di Pietro, Daniele A.; Droniou, Jérôme; Ern, Alexandre SIAM Journal on Numerical Analysis, Vol. 53, Issue 5 https://doi.org/10.1137/140993971	journal	January 2015
The NonConforming Virtual Element Method for the Stokes Equations Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco SIAM Journal on Numerical Analysis, Vol. 54, Issue 6 https://doi.org/10.1137/15M1049531	journal	January 2016
Discontinuous hp -Finite Element Methods for Advection-Diffusion-Reaction Problems Houston, Paul; Schwab, Christoph; Süli, Endre SIAM Journal on Numerical Analysis, Vol. 39, Issue 6 https://doi.org/10.1137/S0036142900374111	journal	January 2002
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo SIAM Journal on Numerical Analysis, Vol. 39, Issue 5 https://doi.org/10.1137/S0036142901384162	journal	January 2002
Basic Principles of Virtual Element Methods BeirÃO Da Veiga, L.; Brezzi, F.; Cangiani, A. Mathematical Models and Methods in Applied Sciences, Vol. 23, Issue 01 https://doi.org/10.1142/S0218202512500492	journal	November 2012
Virtual Element Method for general second-order elliptic problems on polygonal meshes Beirão da Veiga, L.; Brezzi, F.; Marini, L. D. Mathematical Models and Methods in Applied Sciences, Vol. 26, Issue 04 https://doi.org/10.1142/S0218202516500160	journal	February 2016
Design and data structure of fully adaptive, multigrid, finite-element software Rivara, Maria-Cecilia ACM Transactions on Mathematical Software, Vol. 10, Issue 3 https://doi.org/10.1145/1271.1274	journal	August 1984
A New Weak Galerkin Finite Element Scheme for the Brinkman Model Zhai, Qilong; Zhang, Ran; Mu, Lin Communications in Computational Physics, Vol. 19, Issue 5 https://doi.org/10.4208/cicp.scpde14.44s	journal	May 2016

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