Zhang, Yanlong; Zhou, Yanhui A finite volume element solution based on postprocessing technique over arbitrary convex polygonal meshes. (English) Zbl 07793817 Int. J. Numer. Anal. Model. 20, No. 5, 597-617 (2023). MSC: 65-XX 35J25 65N12 65N15 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{Y. Zhou}, Int. J. Numer. Anal. Model. 20, No. 5, 597--617 (2023; Zbl 07793817) Full Text: DOI
Zhang, Yanlong A quadratic serendipity finite volume element method on arbitrary convex polygonal meshes. (English) Zbl 1519.65048 Commun. Comput. Phys. 34, No. 1, 116-131 (2023). MSC: 65N08 65N12 PDFBibTeX XMLCite \textit{Y. Zhang}, Commun. Comput. Phys. 34, No. 1, 116--131 (2023; Zbl 1519.65048) Full Text: DOI
Zhou, Yanhui; Zhang, Yanlong; Wu, Jiming A polygonal finite volume element method for anisotropic diffusion problems. (English) Zbl 07692046 Comput. Math. Appl. 140, 225-236 (2023). MSC: 65N30 65N15 35J25 65N08 65N12 PDFBibTeX XMLCite \textit{Y. Zhou} et al., Comput. Math. Appl. 140, 225--236 (2023; Zbl 07692046) Full Text: DOI
Zhao, Lina; Park, Eun-Jae; Chung, Eric A pressure robust staggered discontinuous Galerkin method for the Stokes equations. (English) Zbl 1504.65262 Comput. Math. Appl. 128, 163-179 (2022). MSC: 65N30 35Q30 76M30 PDFBibTeX XMLCite \textit{L. Zhao} et al., Comput. Math. Appl. 128, 163--179 (2022; Zbl 1504.65262) Full Text: DOI arXiv
Chen, Xinjiang; Wang, Yanqiu A conforming quadratic polygonal element and its application to Stokes equations. (English) Zbl 1499.65649 J. Comput. Math. 40, No. 4, 628-652 (2022). MSC: 65N30 65N12 76D07 76M10 35Q35 PDFBibTeX XMLCite \textit{X. Chen} and \textit{Y. Wang}, J. Comput. Math. 40, No. 4, 628--652 (2022; Zbl 1499.65649) Full Text: DOI
Cao, Juan; Xiao, Yi; Xiao, Yanyang; Chen, Zhonggui; Xue, Fei; Wei, Xiaodong; Zhang, Yongjie Jessica Quadratic serendipity element shape functions on general planar polygons. (English) Zbl 1507.65264 Comput. Methods Appl. Mech. Eng. 392, Article ID 114703, 28 p. (2022). MSC: 65N50 PDFBibTeX XMLCite \textit{J. Cao} et al., Comput. Methods Appl. Mech. Eng. 392, Article ID 114703, 28 p. (2022; Zbl 1507.65264) Full Text: DOI
Arbogast, Todd; Tao, Zhen; Wang, Chuning Direct serendipity and mixed finite elements on convex quadrilaterals. (English) Zbl 1486.65239 Numer. Math. 150, No. 4, 929-974 (2022). MSC: 65N30 65N12 65D05 PDFBibTeX XMLCite \textit{T. Arbogast} et al., Numer. Math. 150, No. 4, 929--974 (2022; Zbl 1486.65239) Full Text: DOI arXiv
Zhang, Weiwei; Hu, Long; Yang, Zongze; Nie, Yufeng Error estimates for the Laplace interpolation on convex polygons. (English) Zbl 1499.65694 Int. J. Numer. Anal. Model. 18, No. 3, 324-338 (2021). MSC: 65N30 65N50 65N15 65N12 PDFBibTeX XMLCite \textit{W. Zhang} et al., Int. J. Numer. Anal. Model. 18, No. 3, 324--338 (2021; Zbl 1499.65694) Full Text: Link
Ge, Qian; Zhang, Xiaoping Numerical solution for third-order two-point boundary value problems with the barycentric rational interpolation collocation method. (English) Zbl 1477.65028 J. Math. 2021, Article ID 6698615, 6 p. (2021). MSC: 65D05 41A05 PDFBibTeX XMLCite \textit{Q. Ge} and \textit{X. Zhang}, J. Math. 2021, Article ID 6698615, 6 p. (2021; Zbl 1477.65028) Full Text: DOI
Gupta, Prashant; Krishnamoorthy, Bala Euler transformation of polyhedral complexes. (English) Zbl 1508.68381 Int. J. Comput. Geom. Appl. 30, No. 3-4, 183-211 (2020). MSC: 68U03 05C10 55U10 PDFBibTeX XMLCite \textit{P. Gupta} and \textit{B. Krishnamoorthy}, Int. J. Comput. Geom. Appl. 30, No. 3--4, 183--211 (2020; Zbl 1508.68381) Full Text: DOI arXiv
Chen, Wenbin; Wang, Yanqiu \(H^1, H(\text{curl})\) and \(H(\text{div})\) conforming elements on polygon-based prisms and cones. (English) Zbl 1446.65163 Numer. Math. 145, No. 4, 973-1004 (2020). MSC: 65N30 65N50 PDFBibTeX XMLCite \textit{W. Chen} and \textit{Y. Wang}, Numer. Math. 145, No. 4, 973--1004 (2020; Zbl 1446.65163) Full Text: DOI
Huang, Weizhang; Wang, Yanqiu Anisotropic mesh quality measures and adaptation for polygonal meshes. (English) Zbl 1436.65200 J. Comput. Phys. 410, Article ID 109368, 33 p. (2020). MSC: 65N50 PDFBibTeX XMLCite \textit{W. Huang} and \textit{Y. Wang}, J. Comput. Phys. 410, Article ID 109368, 33 p. (2020; Zbl 1436.65200) Full Text: DOI arXiv
Anand, Akash; Ovall, Jeffrey S.; Reynolds, Samuel E.; Weißer, Steffen Trefftz finite elements on curvilinear polygons. (English) Zbl 1440.65173 SIAM J. Sci. Comput. 42, No. 2, A1289-A1316 (2020). MSC: 65N30 65R10 65N12 65N15 65R20 PDFBibTeX XMLCite \textit{A. Anand} et al., SIAM J. Sci. Comput. 42, No. 2, A1289--A1316 (2020; Zbl 1440.65173) Full Text: DOI arXiv
Cao, Shuhao; Chen, Long Anisotropic error estimates of the linear nonconforming virtual element methods. (English) Zbl 1422.65376 SIAM J. Numer. Anal. 57, No. 3, 1058-1081 (2019). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{S. Cao} and \textit{L. Chen}, SIAM J. Numer. Anal. 57, No. 3, 1058--1081 (2019; Zbl 1422.65376) Full Text: DOI arXiv
Wang, Yanqiu A nonconforming Crouzeix-Raviart type finite element on polygonal meshes. (English) Zbl 1403.65144 Math. Comput. 88, No. 315, 237-271 (2019). Reviewer: Jichun Li (Las Vegas) MSC: 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{Y. Wang}, Math. Comput. 88, No. 315, 237--271 (2019; Zbl 1403.65144) Full Text: DOI
Anand, Akash; Ovall, Jeffrey S.; Weißer, Steffen A Nyström-based finite element method on polygonal elements. (English) Zbl 1419.65100 Comput. Math. Appl. 75, No. 11, 3971-3986 (2018). MSC: 65N30 65N38 65R20 35R09 65D30 35J25 PDFBibTeX XMLCite \textit{A. Anand} et al., Comput. Math. Appl. 75, No. 11, 3971--3986 (2018; Zbl 1419.65100) Full Text: DOI arXiv
Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit Functional data approximation on bounded domains using polygonal finite elements. (English) Zbl 1441.65018 Comput. Aided Geom. Des. 63, 149-163 (2018). MSC: 65D10 PDFBibTeX XMLCite \textit{J. Cao} et al., Comput. Aided Geom. Des. 63, 149--163 (2018; Zbl 1441.65018) Full Text: DOI Link
Beirão da Veiga, L.; Chernov, A.; Mascotto, L.; Russo, A. Exponential convergence of the \(hp\) virtual element method in presence of corner singularities. (English) Zbl 1387.65117 Numer. Math. 138, No. 3, 581-613 (2018). Reviewer: Gisbert Stoyan (Budapest) MSC: 65N30 65N12 65N15 65N50 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Numer. Math. 138, No. 3, 581--613 (2018; Zbl 1387.65117) Full Text: DOI arXiv
Monzón, Gabriel Sharp geometric requirements in the Wachspress interpolation error estimate. (English) Zbl 1380.65382 Adv. Pure Appl. Math. 9, No. 1, 29-36 (2018). MSC: 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{G. Monzón}, Adv. Pure Appl. Math. 9, No. 1, 29--36 (2018; Zbl 1380.65382) Full Text: DOI arXiv
Chen, Wenbin; Wang, Yanqiu Minimal degree \(H(\mathrm {curl})\) and \(H(\mathrm {div})\) conforming finite elements on polytopal meshes. (English) Zbl 1364.65244 Math. Comput. 86, No. 307, 2053-2087 (2017). MSC: 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{W. Chen} and \textit{Y. Wang}, Math. Comput. 86, No. 307, 2053--2087 (2017; Zbl 1364.65244) Full Text: DOI arXiv
Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit Construction of scalar and vector finite element families on polygonal and polyhedral meshes. (English) Zbl 1348.65163 Comput. Methods Appl. Math. 16, No. 4, 667-683 (2016). MSC: 65N30 41A30 65D05 41A25 PDFBibTeX XMLCite \textit{A. Gillette} et al., Comput. Methods Appl. Math. 16, No. 4, 667--683 (2016; Zbl 1348.65163) Full Text: DOI arXiv Link
Gillette, Andrew; Rand, Alexander Interpolation error estimates for harmonic coordinates on polytopes. (English) Zbl 1343.31004 ESAIM, Math. Model. Numer. Anal. 50, No. 3, 651-676 (2016). MSC: 31B05 35J05 65D05 PDFBibTeX XMLCite \textit{A. Gillette} and \textit{A. Rand}, ESAIM, Math. Model. Numer. Anal. 50, No. 3, 651--676 (2016; Zbl 1343.31004) Full Text: DOI arXiv Link
Abril Bucero, Marta; Bajaj, Chandrajit; Mourrain, Bernard On the construction of general cubature formula by flat extensions. (English) Zbl 1386.65094 Linear Algebra Appl. 502, 104-125 (2016). MSC: 65D32 15B05 65D30 90C22 PDFBibTeX XMLCite \textit{M. Abril Bucero} et al., Linear Algebra Appl. 502, 104--125 (2016; Zbl 1386.65094) Full Text: DOI arXiv
Antonietti, P. F.; Beirão da Veiga, L.; Scacchi, S.; Verani, M. A \(C^1\) virtual element method for the Cahn-Hilliard equation with polygonal meshes. (English) Zbl 1336.65160 SIAM J. Numer. Anal. 54, No. 1, 34-56 (2016). MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., SIAM J. Numer. Anal. 54, No. 1, 34--56 (2016; Zbl 1336.65160) Full Text: DOI arXiv
Bonelle, Jérôme; Di Pietro, Daniele A.; Ern, Alexandre Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes. (English) Zbl 1417.65197 Comput. Aided Geom. Des. 35-36, 27-41 (2015). MSC: 65N30 65N12 35J25 PDFBibTeX XMLCite \textit{J. Bonelle} et al., Comput. Aided Geom. Des. 35--36, 27--41 (2015; Zbl 1417.65197) Full Text: DOI HAL
Talischi, Cameron A family of \(H(\mathrm{div})\) finite element approximations on polygonal meshes. (English) Zbl 1328.65248 SIAM J. Sci. Comput. 37, No. 2, A1067-A1088 (2015). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{C. Talischi}, SIAM J. Sci. Comput. 37, No. 2, A1067--A1088 (2015; Zbl 1328.65248) Full Text: DOI
Peixoto, Pedro S.; Barros, Saulo R. M. On vector field reconstructions for semi-Lagrangian transport methods on geodesic staggered grids. (English) Zbl 1351.86005 J. Comput. Phys. 273, 185-211 (2014). MSC: 86-08 86A10 76M12 52B99 65N50 PDFBibTeX XMLCite \textit{P. S. Peixoto} and \textit{S. R. M. Barros}, J. Comput. Phys. 273, 185--211 (2014; Zbl 1351.86005) Full Text: DOI
Weißer, Steffen Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM. (English) Zbl 1350.65131 Comput. Math. Appl. 67, No. 7, 1390-1406 (2014). MSC: 65N30 65N38 65N12 65N50 35J25 PDFBibTeX XMLCite \textit{S. Weißer}, Comput. Math. Appl. 67, No. 7, 1390--1406 (2014; Zbl 1350.65131) Full Text: DOI
Floater, Michael S. Wachspress and mean value coordinates. (English) Zbl 1325.65033 Fasshauer, Gregory E. (ed.) et al., Approximation theory XIV: San Antonio 2013. Selected papers based on the presentations at the international conference, San Antonio, TX, USA, April 7–10, 2013. Cham: Springer (ISBN 978-3-319-06403-1/hbk; 978-3-319-06404-8/ebook). Springer Proceedings in Mathematics & Statistics 83, 81-102 (2014). MSC: 65D18 PDFBibTeX XMLCite \textit{M. S. Floater}, Springer Proc. Math. Stat. 83, 81--102 (2014; Zbl 1325.65033) Full Text: DOI
Biabanaki, S. O. R.; Khoei, A. R.; Wriggers, P. Polygonal finite element methods for contact-impact problems on non-conformal meshes. (English) Zbl 1296.74105 Comput. Methods Appl. Mech. Eng. 269, 198-221 (2014). MSC: 74S05 74M20 74M15 PDFBibTeX XMLCite \textit{S. O. R. Biabanaki} et al., Comput. Methods Appl. Mech. Eng. 269, 198--221 (2014; Zbl 1296.74105) Full Text: DOI
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit Quadratic serendipity finite elements on polygons using generalized barycentric coordinates. (English) Zbl 1300.65091 Math. Comput. 83, No. 290, 2691-2716 (2014). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N12 65N15 65N50 PDFBibTeX XMLCite \textit{A. Rand} et al., Math. Comput. 83, No. 290, 2691--2716 (2014; Zbl 1300.65091) Full Text: DOI arXiv
Rjasanow, Sergej; Weißer, Steffen FEM with Trefftz trial functions on polyhedral elements. (English) Zbl 1301.65125 J. Comput. Appl. Math. 263, 202-217 (2014). MSC: 65N30 65N38 PDFBibTeX XMLCite \textit{S. Rjasanow} and \textit{S. Weißer}, J. Comput. Appl. Math. 263, 202--217 (2014; Zbl 1301.65125) Full Text: DOI
Talischi, Cameron; Paulino, Glaucio H. Addressing integration error for polygonal finite elements through polynomial projections: a patch test connection. (English) Zbl 1291.65349 Math. Models Methods Appl. Sci. 24, No. 8, 1701-1727 (2014). MSC: 65N30 65N12 76R99 PDFBibTeX XMLCite \textit{C. Talischi} and \textit{G. H. Paulino}, Math. Models Methods Appl. Sci. 24, No. 8, 1701--1727 (2014; Zbl 1291.65349) Full Text: DOI arXiv
Manzini, Gianmarco; Russo, Alessandro; Sukumar, N. New perspectives on polygonal and polyhedral finite element methods. (English) Zbl 1291.65322 Math. Models Methods Appl. Sci. 24, No. 8, 1665-1699 (2014). MSC: 65N06 65N12 65F05 PDFBibTeX XMLCite \textit{G. Manzini} et al., Math. Models Methods Appl. Sci. 24, No. 8, 1665--1699 (2014; Zbl 1291.65322) Full Text: DOI
Sukumar, N. Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons. (English) Zbl 1286.65168 Comput. Methods Appl. Mech. Eng. 263, 27-41 (2013). MSC: 65N30 65N35 65D30 65D05 PDFBibTeX XMLCite \textit{N. Sukumar}, Comput. Methods Appl. Mech. Eng. 263, 27--41 (2013; Zbl 1286.65168) Full Text: DOI
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit Interpolation error estimates for mean value coordinates over convex polygons. (English) Zbl 1275.41005 Adv. Comput. Math. 39, No. 2, 327-347 (2013). MSC: 41A05 65D05 65N15 65N30 PDFBibTeX XMLCite \textit{A. Rand} et al., Adv. Comput. Math. 39, No. 2, 327--347 (2013; Zbl 1275.41005) Full Text: DOI arXiv Link
Klausen, Runhild A.; Rasmussen, Atgeirr F.; Stephansen, Annette F. Velocity interpolation and streamline tracing on irregular geometries. (English) Zbl 1254.65035 Comput. Geosci. 16, No. 2, 261-276 (2012). MSC: 65D18 76N15 65N30 76M10 76M20 PDFBibTeX XMLCite \textit{R. A. Klausen} et al., Comput. Geosci. 16, No. 2, 261--276 (2012; Zbl 1254.65035) Full Text: DOI