Wang, Junping; Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou; Zhu, Peng Two-order superconvergence for a weak Galerkin method on rectangular and cuboid grids. (English) Zbl 07779729 Numer. Methods Partial Differ. Equations 39, No. 1, 744-758 (2023). MSC: 65N30 65N12 65N15 35J25 PDFBibTeX XMLCite \textit{J. Wang} et al., Numer. Methods Partial Differ. Equations 39, No. 1, 744--758 (2023; Zbl 07779729) Full Text: DOI
Zhu, Peng; Xie, Shenglan A weak Galerkin method and its two-grid algorithm for the quasi-linear elliptic problems of non-monotone type. (English) Zbl 07776952 Numer. Methods Partial Differ. Equations 39, No. 2, 1042-1066 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{P. Zhu} and \textit{S. Xie}, Numer. Methods Partial Differ. Equations 39, No. 2, 1042--1066 (2023; Zbl 07776952) Full Text: DOI arXiv
Zhu, Peng; Xie, Shenglan; Wang, Xiaoshen A stabilizer-free \(C^0\) weak Galerkin method for the biharmonic equations. (English) Zbl 1509.65120 Sci. China, Math. 66, No. 3, 627-646 (2023). MSC: 65N30 65N15 31A30 PDFBibTeX XMLCite \textit{P. Zhu} et al., Sci. China, Math. 66, No. 3, 627--646 (2023; Zbl 1509.65120) Full Text: DOI arXiv
Toprakseven, Şuayip; Zhu, Peng Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms. (English) Zbl 1511.65072 Appl. Math. Comput. 441, Article ID 127683, 24 p. (2023). MSC: 65L60 65L10 65L11 65L20 65L70 PDFBibTeX XMLCite \textit{Ş. Toprakseven} and \textit{P. Zhu}, Appl. Math. Comput. 441, Article ID 127683, 24 p. (2023; Zbl 1511.65072) Full Text: DOI
Liu, Kaifang; Zhu, Peng Analysis of a weak Galerkin method for second-order elliptic equations with minimal regularity on polytopal meshes. (English) Zbl 1498.65203 J. Comput. Appl. Math. 420, Article ID 114744, 14 p. (2023). MSC: 65N30 35J15 65N25 65N15 35B65 PDFBibTeX XMLCite \textit{K. Liu} and \textit{P. Zhu}, J. Comput. Appl. Math. 420, Article ID 114744, 14 p. (2023; Zbl 1498.65203) Full Text: DOI
Zhu, Peng; Xie, Shenglan Supercloseness and postprocessing of stabilizer-free weak Galerkin finite element approximations for parabolic problems. (English) Zbl 1524.65634 Comput. Math. Appl. 119, 79-88 (2022). MSC: 65M60 65N30 65N15 65M15 65N12 65M06 PDFBibTeX XMLCite \textit{P. Zhu} and \textit{S. Xie}, Comput. Math. Appl. 119, 79--88 (2022; Zbl 1524.65634) Full Text: DOI
Xie, Shenglan; Zhu, Peng Superconvergence of a WG method for the Stokes equations with continuous pressure. (English) Zbl 1502.65221 Appl. Numer. Math. 179, 27-38 (2022). MSC: 65N30 65N12 65N15 76D07 35Q35 PDFBibTeX XMLCite \textit{S. Xie} and \textit{P. Zhu}, Appl. Numer. Math. 179, 27--38 (2022; Zbl 1502.65221) Full Text: DOI
Ye, Xiu; Zhang, Shangyou; Zhu, Peng Development of a LDG method on polytopal mesh with optimal order of convergence. (English) Zbl 1490.65293 J. Comput. Appl. Math. 410, Article ID 114179, 10 p. (2022). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{X. Ye} et al., J. Comput. Appl. Math. 410, Article ID 114179, 10 p. (2022; Zbl 1490.65293) Full Text: DOI
Zhu, Peng; Xie, Shenglan Superconvergent weak Galerkin methods for non-self adjoint and indefinite elliptic problems. (English) Zbl 1484.65310 Appl. Numer. Math. 172, 300-314 (2022). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{P. Zhu} and \textit{S. Xie}, Appl. Numer. Math. 172, 300--314 (2022; Zbl 1484.65310) Full Text: DOI
Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou; Zhu, Peng A weak Galerkin least squares finite element method of Cauchy problem for Poisson equation. (English) Zbl 1490.65289 J. Comput. Appl. Math. 401, Article ID 113767, 9 p. (2022). MSC: 65N30 35B45 35J50 65N12 65N15 PDFBibTeX XMLCite \textit{X. Wang} et al., J. Comput. Appl. Math. 401, Article ID 113767, 9 p. (2022; Zbl 1490.65289) Full Text: DOI
Toprakseven, Şuayip; Zhu, Peng Uniform convergent modified weak Galerkin method for convection-dominated two-point boundary value problems. (English) Zbl 1493.65232 Turk. J. Math. 45, No. 6, 2703-2730 (2021). MSC: 65N30 PDFBibTeX XMLCite \textit{Ş. Toprakseven} and \textit{P. Zhu}, Turk. J. Math. 45, No. 6, 2703--2730 (2021; Zbl 1493.65232) Full Text: DOI
Al-Taweel, Ahmed; Hussain, Saqib; Lin, Runchang; Zhu, Peng A stabilizer free weak Galerkin finite element method for general second-order elliptic problem. (English) Zbl 1499.65641 Int. J. Numer. Anal. Model. 18, No. 3, 311-323 (2021). MSC: 65N30 65N15 35J50 65N12 35J15 PDFBibTeX XMLCite \textit{A. Al-Taweel} et al., Int. J. Numer. Anal. Model. 18, No. 3, 311--323 (2021; Zbl 1499.65641) Full Text: Link
Xie, Shenglan; Han, Maoan; Zhu, Peng A posteriori error estimate of weak Galerkin FEM for second order elliptic problem with mixed boundary condition. (English) Zbl 1476.65311 Discrete Contin. Dyn. Syst., Ser. B 26, No. 10, 5217-5226 (2021). MSC: 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{S. Xie} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 10, 5217--5226 (2021; Zbl 1476.65311) Full Text: DOI
Ye, Xiu; Zhang, Shangyou; Zhu, Peng A weak Galerkin finite element method for nonlinear conservation laws. (English) Zbl 1456.65127 Electron. Res. Arch. 29, No. 1, 1897-1923 (2021). MSC: 65M60 65N30 65M06 65N15 35L50 35L65 PDFBibTeX XMLCite \textit{X. Ye} et al., Electron. Res. Arch. 29, No. 1, 1897--1923 (2021; Zbl 1456.65127) Full Text: DOI
Cui, Jintao; Gao, Fuzheng; Sun, Zhengjia; Zhu, Peng A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh. (English) Zbl 07771405 Numer. Methods Partial Differ. Equations 36, No. 3, 601-616 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{J. Cui} et al., Numer. Methods Partial Differ. Equations 36, No. 3, 601--616 (2020; Zbl 07771405) Full Text: DOI
Zhu, Peng; Wang, Xiaoshen A least square based weak Galerkin finite element method for second order elliptic equations in non-divergence form. (English) Zbl 1513.65478 Acta Math. Sci., Ser. B, Engl. Ed. 40, No. 5, 1553-1562 (2020). MSC: 65N30 65N15 35J15 65K10 65N12 PDFBibTeX XMLCite \textit{P. Zhu} and \textit{X. Wang}, Acta Math. Sci., Ser. B, Engl. Ed. 40, No. 5, 1553--1562 (2020; Zbl 1513.65478) Full Text: DOI
Zhu, Peng; Xie, Shenglan A uniformly convergent weak Galerkin finite element method on Shishkin mesh for 1d convection-diffusion problem. (English) Zbl 1452.65365 J. Sci. Comput. 85, No. 2, Paper No. 34, 21 p. (2020). MSC: 65N30 65N15 65N12 35B25 65L11 65L60 PDFBibTeX XMLCite \textit{P. Zhu} and \textit{S. Xie}, J. Sci. Comput. 85, No. 2, Paper No. 34, 21 p. (2020; Zbl 1452.65365) Full Text: DOI
Gao, Fuzheng; Zhang, Shangyou; Zhu, Peng Modified weak Galerkin method with weakly imposed boundary condition for convection-dominated diffusion equations. (English) Zbl 1446.76128 Appl. Numer. Math. 157, 490-504 (2020). MSC: 76M10 76R50 65N12 65N15 PDFBibTeX XMLCite \textit{F. Gao} et al., Appl. Numer. Math. 157, 490--504 (2020; Zbl 1446.76128) Full Text: DOI
Ye, Xiu; Zhang, Shangyou; Zhu, Peng A discontinuous Galerkin least-squares method for div-curl systems. (English) Zbl 1428.65097 J. Comput. Appl. Math. 367, Article ID 112474, 10 p. (2020). MSC: 65N30 65N15 76D07 35B45 35J50 PDFBibTeX XMLCite \textit{X. Ye} et al., J. Comput. Appl. Math. 367, Article ID 112474, 10 p. (2020; Zbl 1428.65097) Full Text: DOI
Xie, Shenglan; Zhu, Peng; Wang, Xiaoshen Error analysis of weak Galerkin finite element methods for time-dependent convection-diffusion equations. (English) Zbl 1407.65206 Appl. Numer. Math. 137, 19-33 (2019). MSC: 65M60 65M15 76M10 PDFBibTeX XMLCite \textit{S. Xie} et al., Appl. Numer. Math. 137, 19--33 (2019; Zbl 1407.65206) Full Text: DOI
Hussain, Saqib; Malluwawadu, Nolisa; Zhu, Peng A weak Galerkin finite element method for the second order elliptic problems with mixed boundary conditions. (English) Zbl 1453.65408 J. Appl. Anal. Comput. 8, No. 5, 1452-1463 (2018). MSC: 65N30 65N15 35J50 PDFBibTeX XMLCite \textit{S. Hussain} et al., J. Appl. Anal. Comput. 8, No. 5, 1452--1463 (2018; Zbl 1453.65408) Full Text: DOI
Lin, Runchang; Ye, Xiu; Zhang, Shangyou; Zhu, Peng A weak Galerkin finite element method for singularly perturbed convection-diffusion-reaction problems. (English) Zbl 1448.65239 SIAM J. Numer. Anal. 56, No. 3, 1482-1497 (2018). MSC: 65N30 65N15 35J25 35B25 PDFBibTeX XMLCite \textit{R. Lin} et al., SIAM J. Numer. Anal. 56, No. 3, 1482--1497 (2018; Zbl 1448.65239) Full Text: DOI