A family of interior-penalized weak Galerkin methods for second-order elliptic equations

Kaifang Liu;  ; Lunji Song

doi:10.3934/math.2021030

A family of interior-penalized weak Galerkin methods for second-order elliptic equations

AIMS Mathematics ◽

10.3934/math.2021030 ◽

2021 ◽

Vol 6 (1) ◽

pp. 500-517

Author(s):

Kaifang Liu ◽

◽

Lunji Song

Keyword(s):

Elliptic Equations ◽

Second Order ◽

Galerkin Methods ◽

Weak Galerkin ◽

Second Order Elliptic Equations

Download Full-text

$(1+s)$-Order Convergence Analysis of Weak Galerkin Finite Element Methods for Second Order Elliptic Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.oa-2020-0020 ◽

2021 ◽

Vol 13 (3) ◽

pp. 554-568

Author(s):

global sci

Keyword(s):

Finite Element ◽

Convergence Analysis ◽

Finite Element Methods ◽

Elliptic Equations ◽

Second Order ◽

Order Convergence ◽

Weak Galerkin ◽

Galerkin Finite Element ◽

Galerkin Finite Element Methods ◽

Second Order Elliptic Equations

Download Full-text

A Least Square Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence Form

Acta Mathematica Scientia ◽

10.1007/s10473-020-0521-y ◽

2020 ◽

Vol 40 (5) ◽

pp. 1553-1562

Author(s):

Peng Zhu ◽

Xiaoshen Wang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elliptic Equations ◽

Divergence Form ◽

Second Order ◽

Least Square ◽

Galerkin Finite Element Method ◽

Weak Galerkin ◽

Galerkin Finite Element ◽

Second Order Elliptic Equations

Download Full-text

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

SIAM Journal on Scientific Computing ◽

10.1137/16m1083244 ◽

2017 ◽

Vol 39 (4) ◽

pp. A1531-A1557 ◽

Cited By ~ 4

Author(s):

Lin Mu ◽

Junping Wang ◽

Xiu Ye

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Least Squares ◽

Elliptic Equations ◽

Second Order ◽

Galerkin Finite Element Method ◽

Weak Galerkin ◽

Galerkin Finite Element ◽

Second Order Elliptic Equations ◽

Element Method

Download Full-text

A computational study of the weak Galerkin method for second-order elliptic equations

Numerical Algorithms ◽

10.1007/s11075-012-9651-1 ◽

2012 ◽

Vol 63 (4) ◽

pp. 753-777 ◽

Cited By ~ 54

Author(s):

Lin Mu ◽

Junping Wang ◽

Yanqiu Wang ◽

Xiu Ye

Keyword(s):

Galerkin Method ◽

Elliptic Equations ◽

Computational Study ◽

Second Order ◽

Weak Galerkin ◽

Second Order Elliptic Equations

Download Full-text

A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form

Mathematics of Computation ◽

10.1090/mcom/3220 ◽

2017 ◽

Vol 87 (310) ◽

pp. 515-545 ◽

Cited By ~ 30

Author(s):

Chunmei Wang ◽

Junping Wang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elliptic Equations ◽

Divergence Form ◽

Second Order ◽

Galerkin Finite Element Method ◽

Weak Galerkin ◽

Galerkin Finite Element ◽

Primal Dual ◽

Second Order Elliptic Equations

Download Full-text

A penalized weak Galerkin spectral element method for second order elliptic equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113228 ◽

2021 ◽

Vol 386 ◽

pp. 113228

Author(s):

Jiajia Pan ◽

Huiyuan Li

Keyword(s):

Elliptic Equations ◽

Spectral Element Method ◽

Spectral Element ◽

Second Order ◽

Weak Galerkin ◽

Second Order Elliptic Equations ◽

Element Method

Download Full-text

Properties of a solution of the Dirichlet problem for second-order elliptic equations in a class of domains with nonsmooth boundary. I

Lithuanian Mathematical Journal ◽

10.1007/bf00966149 ◽

1987 ◽

Vol 26 (2) ◽

pp. 153-163

Author(s):

K. Pileckas ◽

K. Samaitis

Keyword(s):

Dirichlet Problem ◽

Elliptic Equations ◽

Second Order ◽

Nonsmooth Boundary ◽

Second Order Elliptic Equations

Download Full-text

A posteriori error estimates for weak Galerkin methods for second order elliptic problems on polygonal meshes

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.12.005 ◽

2021 ◽

Vol 161 ◽

pp. 510-524

Author(s):

Shipeng Xu

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Elliptic Problems ◽

Posteriori Error ◽

Second Order ◽

Galerkin Methods ◽

A Posteriori ◽

Weak Galerkin ◽

A Posteriori Error ◽

Second Order Elliptic Problems

Download Full-text

Regularity of the generalized solutions of the first boundary-value problem for quasilinear degenerate second-order elliptic equations

Journal of Soviet Mathematics ◽

10.1007/bf01788913 ◽

1984 ◽

Vol 25 (1) ◽

pp. 815-832 ◽

Cited By ~ 1

Author(s):

A. V. Ivanov

Keyword(s):

Boundary Value Problem ◽

Elliptic Equations ◽

Boundary Value ◽

Second Order ◽

Generalized Solutions ◽

Second Order Elliptic Equations

Download Full-text

On Regularity and Existence of Viscosity Solutions of Nonlinear Second Order, Elliptic Equations

Partial Differential Equations and the Calculus of Variations ◽

10.1007/978-1-4684-9196-8_41 ◽

1989 ◽

pp. 939-957 ◽

Cited By ~ 6

Author(s):

Neil S. Trudinger

Keyword(s):

Viscosity Solutions ◽

Elliptic Equations ◽

Second Order ◽

Regularity And Existence ◽

Second Order Elliptic Equations

Download Full-text