Kong, Wang; Hong, Zhenying; Yuan, Guangwei; Sheng, Zhiqiang Extremum-preserving correction of the nine-point scheme for diffusion equation on distorted meshes. (English) Zbl 1513.65450 Adv. Appl. Math. Mech. 15, No. 2, 402-427 (2023). MSC: 65N08 65N50 76M12 35B50 PDFBibTeX XMLCite \textit{W. Kong} et al., Adv. Appl. Math. Mech. 15, No. 2, 402--427 (2023; Zbl 1513.65450) Full Text: DOI
Wu, Xiaoxin; Pan, Kejia; Li, Jin; Yu, Yunlong; Yuan, Guangwei; Ren, Zhengyong A robust, interpolation-free and monotone finite volume scheme for diffusion equations on arbitrary quadrilateral meshes. (English) Zbl 07768046 Int. J. Numer. Methods Eng. 123, No. 16, 3631-3657 (2022). MSC: 65Nxx 65Mxx 35Jxx PDFBibTeX XMLCite \textit{X. Wu} et al., Int. J. Numer. Methods Eng. 123, No. 16, 3631--3657 (2022; Zbl 07768046) Full Text: DOI
Pan, Kejia; Wu, Xiaoxin; Yu, Yunlong; Sheng, Zhiqiang; Yuan, Guangwei Extrapolation cascadic multigrid method for cell-centered FV discretization of diffusion equations with strongly discontinuous and anisotropic coefficients. (English) Zbl 1486.65281 Commun. Comput. Phys. 31, No. 5, 1561-1584 (2022). MSC: 65N55 65N08 PDFBibTeX XMLCite \textit{K. Pan} et al., Commun. Comput. Phys. 31, No. 5, 1561--1584 (2022; Zbl 1486.65281) Full Text: DOI
Pan, Kejia; Li, Jin; Wu, Xiaoxin; Yuan, Guangwei; Yue, Xiaoqiang A new finite volume scheme with gradient transfer method for solving diffusion problems on the distorted hexahedral meshes. (English) Zbl 1484.65287 Comput. Geosci. 26, No. 2, 279-294 (2022). MSC: 65N08 65N12 PDFBibTeX XMLCite \textit{K. Pan} et al., Comput. Geosci. 26, No. 2, 279--294 (2022; Zbl 1484.65287) Full Text: DOI
Xu, Jinjing; Zhao, Fei; Sheng, Zhiqiang; Yuan, Guangwei A nonlinear finite volume scheme preserving maximum principle for diffusion equations. (English) Zbl 1473.65265 Commun. Comput. Phys. 29, No. 3, 747-766 (2021). MSC: 65N08 65M22 PDFBibTeX XMLCite \textit{J. Xu} et al., Commun. Comput. Phys. 29, No. 3, 747--766 (2021; Zbl 1473.65265) Full Text: DOI
Zhao, Fei; Sheng, Zhiqiang; Yuan, Guangwei A monotone combination scheme of diffusion equations on polygonal meshes. (English) Zbl 07806604 ZAMM, Z. Angew. Math. Mech. 100, No. 5, Article ID e201900320, 25 p. (2020). MSC: 65Nxx 65Mxx 35Jxx PDFBibTeX XMLCite \textit{F. Zhao} et al., ZAMM, Z. Angew. Math. Mech. 100, No. 5, Article ID e201900320, 25 p. (2020; Zbl 07806604) Full Text: DOI
Zhao, Fei; Lai, Xiang; Yuan, Guangwei; Sheng, Zhiqiang A new interpolation for auxiliary unknowns of the monotone finite volume scheme for 3D diffusion equations. (English) Zbl 1473.65151 Commun. Comput. Phys. 27, No. 4, 1201-1233 (2020). MSC: 65M08 65M12 65B99 PDFBibTeX XMLCite \textit{F. Zhao} et al., Commun. Comput. Phys. 27, No. 4, 1201--1233 (2020; Zbl 1473.65151) Full Text: DOI
Yu, Yao; Yuan, Guangwei; Sheng, Zhiqiang; Li, Yonghai The finite volume scheme preserving maximum principle for diffusion equations with discontinuous coefficient. (English) Zbl 1437.65168 Comput. Math. Appl. 79, No. 8, 2168-2188 (2020). MSC: 65N08 35R05 76R50 PDFBibTeX XMLCite \textit{Y. Yu} et al., Comput. Math. Appl. 79, No. 8, 2168--2188 (2020; Zbl 1437.65168) Full Text: DOI
Zhang, Qi; Sheng, Zhiqiang; Yuan, Guangwei A monotone finite volume scheme for diffusion equations on general non-conforming meshes. (English) Zbl 1426.65160 Appl. Math. Comput. 311, 300-313 (2017). MSC: 65N08 PDFBibTeX XMLCite \textit{Q. Zhang} et al., Appl. Math. Comput. 311, 300--313 (2017; Zbl 1426.65160) Full Text: DOI
Chen, Xingding; Yuan, Guangwei; Yu, Yunlong Discrete maximum principle based on repair technique for finite element scheme of anisotropic diffusion problems. (English) Zbl 1488.65607 Adv. Appl. Math. Mech. 6, No. 6, 849-866 (2014). MSC: 65N30 35B45 65N15 PDFBibTeX XMLCite \textit{X. Chen} et al., Adv. Appl. Math. Mech. 6, No. 6, 849--866 (2014; Zbl 1488.65607) Full Text: DOI
Sheng, Zhiqiang; Yuan, Guangwei An improved monotone finite volume scheme for diffusion equation on polygonal meshes. (English) Zbl 1242.65219 J. Comput. Phys. 231, No. 9, 3739-3754 (2012). MSC: 65N08 35J25 65N50 PDFBibTeX XMLCite \textit{Z. Sheng} and \textit{G. Yuan}, J. Comput. Phys. 231, No. 9, 3739--3754 (2012; Zbl 1242.65219) Full Text: DOI
Sheng, Zhiqiang; Yuan, Guangwei The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes. (English) Zbl 1218.65120 J. Comput. Phys. 230, No. 7, 2588-2604 (2011). MSC: 65N08 35J25 65N50 PDFBibTeX XMLCite \textit{Z. Sheng} and \textit{G. Yuan}, J. Comput. Phys. 230, No. 7, 2588--2604 (2011; Zbl 1218.65120) Full Text: DOI
Wu, Jiming; Dai, Zihuan; Gao, Zhiming; Yuan, Guangwei Linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes. (English) Zbl 1187.65119 J. Comput. Phys. 229, No. 9, 3382-3401 (2010). MSC: 65N06 35J25 65N50 PDFBibTeX XMLCite \textit{J. Wu} et al., J. Comput. Phys. 229, No. 9, 3382--3401 (2010; Zbl 1187.65119) Full Text: DOI
Zhao, Qiang; Yuan, Guangwei Analysis and construction of cell-centered finite volume scheme for diffusion equations on distorted meshes. (English) Zbl 1229.76065 Comput. Methods Appl. Mech. Eng. 198, No. 37-40, 3039-3050 (2009). MSC: 76M12 76R50 PDFBibTeX XMLCite \textit{Q. Zhao} and \textit{G. Yuan}, Comput. Methods Appl. Mech. Eng. 198, No. 37--40, 3039--3050 (2009; Zbl 1229.76065) Full Text: DOI
Chang, Lina; Yuan, Guangwei Cell-centered finite volume methods with flexible stencils for diffusion equations on general nonconforming meshes. (English) Zbl 1227.76042 Comput. Methods Appl. Mech. Eng. 198, No. 17-20, 1638-1646 (2009). MSC: 76M12 76R50 PDFBibTeX XMLCite \textit{L. Chang} and \textit{G. Yuan}, Comput. Methods Appl. Mech. Eng. 198, No. 17--20, 1638--1646 (2009; Zbl 1227.76042) Full Text: DOI
Sheng, Zhiqiang; Yuan, Guangwei A finite volume scheme for diffusion equations on distorted quadrilateral meshes. (English) Zbl 1375.82100 Transp. Theory Stat. Phys. 37, No. 2-4, 171-207 (2008). MSC: 82C80 65N06 76M12 PDFBibTeX XMLCite \textit{Z. Sheng} and \textit{G. Yuan}, Transp. Theory Stat. Phys. 37, No. 2--4, 171--207 (2008; Zbl 1375.82100) Full Text: DOI
Yuan, GuangWei; Sheng, ZhiQiang Calculating the vertex unknowns of nine point scheme on quadrilateral meshes for diffusion equation. (English) Zbl 1161.65070 Sci. China, Ser. A 51, No. 8, 1522-1536 (2008). Reviewer: K. N. Shukla (Coimbatore) MSC: 65M06 65M12 65M50 35K05 35J25 65N30 65N12 PDFBibTeX XMLCite \textit{G. Yuan} and \textit{Z. Sheng}, Sci. China, Ser. A 51, No. 8, 1522--1536 (2008; Zbl 1161.65070) Full Text: DOI
Yuan, Guangwei; Sheng, Zhiqiang Monotone finite volume schemes for diffusion equations on polygonal meshes. (English) Zbl 1147.65069 J. Comput. Phys. 227, No. 12, 6288-6312 (2008). MSC: 65M06 35K05 65M50 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{G. Yuan} and \textit{Z. Sheng}, J. Comput. Phys. 227, No. 12, 6288--6312 (2008; Zbl 1147.65069) Full Text: DOI
Yuan, Guangwei; Sheng, Zhiqiang Analysis of accuracy of a finite volume scheme for diffusion equations on distorted meshes. (English) Zbl 1119.65084 J. Comput. Phys. 224, No. 2, 1170-1189 (2007). Reviewer: Nicolae Pop (Baia Mare) MSC: 65M06 65M12 76M12 65M55 65M70 35K15 PDFBibTeX XMLCite \textit{G. Yuan} and \textit{Z. Sheng}, J. Comput. Phys. 224, No. 2, 1170--1189 (2007; Zbl 1119.65084) Full Text: DOI