Li, Meng; Zhao, Jikun; Chen, Shaochun Unconditional error analysis of VEMs for a generalized nonlinear Schrödinger equation. (English) Zbl 07806682 J. Comput. Math. 42, No. 2, 500-543 (2024). MSC: 65N35 65N12 76D07 65N15 PDFBibTeX XMLCite \textit{M. Li} et al., J. Comput. Math. 42, No. 2, 500--543 (2024; Zbl 07806682) Full Text: DOI
Adak, D.; Mora, D.; Silgado, A. The Morley-type virtual element method for the Navier-Stokes equations in stream-function form. (English) Zbl 07796644 Comput. Methods Appl. Mech. Eng. 419, Article ID 116573, 28 p. (2024). MSC: 65N30 65N12 76D05 65N15 PDFBibTeX XMLCite \textit{D. Adak} et al., Comput. Methods Appl. Mech. Eng. 419, Article ID 116573, 28 p. (2024; Zbl 07796644) Full Text: DOI arXiv
Mishra, Sudheer; Natarajan, E. Local projection stabilization virtual element method for the convection-diffusion equation with nonlinear reaction term. (English) Zbl 07801665 Comput. Math. Appl. 152, 181-198 (2023). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{S. Mishra} and \textit{E. Natarajan}, Comput. Math. Appl. 152, 181--198 (2023; Zbl 07801665) Full Text: DOI
Kravetc, Tatiana Blending spline surfaces over polygon mesh and their application to isogeometric analysis. (English) Zbl 07750309 Comput. Math. Appl. 149, 84-98 (2023). MSC: 65N30 74S05 65D07 65D05 76M10 PDFBibTeX XMLCite \textit{T. Kravetc}, Comput. Math. Appl. 149, 84--98 (2023; Zbl 07750309) Full Text: DOI
Vengatesan, S.; Natarajan, Sundararajan; Jeyakarthikeyan, P. V. \(n+1\) Integration scheme for polygonal elements using Richardson extrapolation. (English) Zbl 07628013 Math. Comput. Simul. 205, 659-677 (2023). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{S. Vengatesan} et al., Math. Comput. Simul. 205, 659--677 (2023; Zbl 07628013) 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
Manzini, Gianmarco; Mazzia, Annamaria Conforming virtual element approximations of the two-dimensional Stokes problem. (English) Zbl 1502.65212 Appl. Numer. Math. 181, 176-203 (2022). MSC: 65N30 65N12 65N15 76D07 76M10 35Q35 PDFBibTeX XMLCite \textit{G. Manzini} and \textit{A. Mazzia}, Appl. Numer. Math. 181, 176--203 (2022; Zbl 1502.65212) 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
Manzini, Gianmarco; Mazzia, Annamaria A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem. (English) Zbl 1492.65324 J. Comput. Dyn. 9, No. 2, 207-238 (2022). Reviewer: Francesca Gardini (Pavia) MSC: 65N30 65N22 65N12 65N15 76D07 76M10 35B45 35Q35 PDFBibTeX XMLCite \textit{G. Manzini} and \textit{A. Mazzia}, J. Comput. Dyn. 9, No. 2, 207--238 (2022; Zbl 1492.65324) Full Text: DOI arXiv
Perot, J. Blair; Chartrand, Chris A mimetic method for polygons. (English) Zbl 07508458 J. Comput. Phys. 424, Article ID 109853, 21 p. (2021). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{J. B. Perot} and \textit{C. Chartrand}, J. Comput. Phys. 424, Article ID 109853, 21 p. (2021; Zbl 07508458) Full Text: DOI
Vu-Huu, T.; Le-Thanh, C.; Nguyen-Xuan, H.; Wahab, M. Abdel Equal-order polygonal analysis for fluid computation in curved domain. (English) Zbl 07446900 Int. J. Comput. Methods 18, No. 5, Article ID 2040003, 10 p. (2021). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{T. Vu-Huu} et al., Int. J. Comput. Methods 18, No. 5, Article ID 2040003, 10 p. (2021; Zbl 07446900) Full Text: DOI
Liu, Mingyang; Gao, Guangjun; Zhu, Huifen; Jiang, Chen; Liu, Guirong A cell-based smoothed finite element method for arbitrary polygonal element to solve incompressible laminar flow. (English) Zbl 07446684 Int. J. Comput. Methods 18, No. 7, Article ID 2150017, 28 p. (2021). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{M. Liu} et al., Int. J. Comput. Methods 18, No. 7, Article ID 2150017, 28 p. (2021; Zbl 07446684) Full Text: DOI
Attene, Marco; Biasotti, Silvia; Bertoluzza, Silvia; Cabiddu, Daniela; Livesu, Marco; Patanè, Giuseppe; Pennacchio, Micol; Prada, Daniele; Spagnuolo, Michela Benchmarking the geometrical robustness of a virtual element Poisson solver. (English) Zbl 07431576 Math. Comput. Simul. 190, 1392-1414 (2021). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{M. Attene} et al., Math. Comput. Simul. 190, 1392--1414 (2021; Zbl 07431576) Full Text: DOI
Li, Yang; Feng, Minfu A local projection stabilization virtual element method for convection-diffusion-reaction equation. (English) Zbl 1510.76090 Appl. Math. Comput. 411, Article ID 126536, 15 p. (2021). MSC: 76M10 65M60 35K57 PDFBibTeX XMLCite \textit{Y. Li} and \textit{M. Feng}, Appl. Math. Comput. 411, Article ID 126536, 15 p. (2021; Zbl 1510.76090) Full Text: DOI
Lepe, Felipe; Mora, David; Rivera, Gonzalo; Velásquez, Iván A virtual element method for the Steklov eigenvalue problem allowing small edges. (English) Zbl 1479.35677 J. Sci. Comput. 88, No. 2, Paper No. 44, 21 p. (2021). MSC: 35Q35 65N25 65N30 65N50 65N12 65N15 76B15 35A15 PDFBibTeX XMLCite \textit{F. Lepe} et al., J. Sci. Comput. 88, No. 2, Paper No. 44, 21 p. (2021; Zbl 1479.35677) Full Text: DOI arXiv
Antonietti, Paola F.; Facciolà, Chiara; Verani, Marco Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids. (English) Zbl 1489.76036 Math. Eng. (Springfield) 2, No. 2, 340-385 (2020). MSC: 76M10 76S05 65N30 65N15 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Math. Eng. (Springfield) 2, No. 2, 340--385 (2020; Zbl 1489.76036) Full Text: DOI
Antonietti, Paola F.; Bonaldi, Francesco; Mazzieri, Ilario A high-order discontinuous Galerkin approach to the elasto-acoustic problem. (English) Zbl 1441.74228 Comput. Methods Appl. Mech. Eng. 358, Article ID 112634, 29 p. (2020). MSC: 74S05 76M10 65M12 65M60 74J05 76Q05 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Comput. Methods Appl. Mech. Eng. 358, Article ID 112634, 29 p. (2020; Zbl 1441.74228) Full Text: DOI arXiv
Dassi, F.; Vacca, G. Bricks for the mixed high-order virtual element method: projectors and differential operators. (English) Zbl 1437.65184 Appl. Numer. Math. 155, 140-159 (2020). MSC: 65N30 76D07 76S05 PDFBibTeX XMLCite \textit{F. Dassi} and \textit{G. Vacca}, Appl. Numer. Math. 155, 140--159 (2020; Zbl 1437.65184) Full Text: DOI arXiv
Natarajan, Sundararajan On the application of polygonal finite element method for Stokes flow – a comparison between equal order and different order approximation. (English) Zbl 1505.65295 Comput. Aided Geom. Des. 77, Article ID 101813, 11 p. (2020). MSC: 65N30 65N12 74S05 76M10 PDFBibTeX XMLCite \textit{S. Natarajan}, Comput. Aided Geom. Des. 77, Article ID 101813, 11 p. (2020; Zbl 1505.65295) Full Text: DOI
Vu-Huu, T.; Le-Thanh, C.; Nguyen-Xuan, H.; Abdel-Wahab, M. An equal-order mixed polygonal finite element for two-dimensional incompressible Stokes flows. (English) Zbl 1477.76056 Eur. J. Mech., B, Fluids 79, 92-108 (2020). MSC: 76M10 76D07 PDFBibTeX XMLCite \textit{T. Vu-Huu} et al., Eur. J. Mech., B, Fluids 79, 92--108 (2020; Zbl 1477.76056) Full Text: DOI
Li, Qiuqi; Jiang, Lijian A multiscale virtual element method for elliptic problems in heterogeneous porous media. (English) Zbl 1452.65349 J. Comput. Phys. 388, 394-415 (2019). MSC: 65N30 76S05 76M10 65N55 65F55 65Z05 PDFBibTeX XMLCite \textit{Q. Li} and \textit{L. Jiang}, J. Comput. Phys. 388, 394--415 (2019; Zbl 1452.65349) Full Text: DOI
Vu-Huu, T.; Le-Thanh, C.; Nguyen-Xuan, H.; Abdel-Wahab, M. A high-order mixed polygonal finite element for incompressible Stokes flow analysis. (English) Zbl 1441.76073 Comput. Methods Appl. Mech. Eng. 356, 175-198 (2019). MSC: 76M10 65N30 76D07 PDFBibTeX XMLCite \textit{T. Vu-Huu} et al., Comput. Methods Appl. Mech. Eng. 356, 175--198 (2019; Zbl 1441.76073) Full Text: DOI
Cicuttin, Matteo; Ern, Alexandre; Lemaire, Simon A hybrid high-order method for highly oscillatory elliptic problems. (English) Zbl 1434.65246 Comput. Methods Appl. Math. 19, No. 4, 723-748 (2019). MSC: 65N30 65N08 76R50 65N85 PDFBibTeX XMLCite \textit{M. Cicuttin} et al., Comput. Methods Appl. Math. 19, No. 4, 723--748 (2019; Zbl 1434.65246) Full Text: DOI arXiv
Manzini, Gianmarco; Maguolo, Gianluca; Putti, Mario The high-order mixed mimetic finite difference method for time-dependent diffusion problems. (English) Zbl 1428.65013 J. Sci. Comput. 80, No. 3, 1805-1830 (2019); correction ibid. 80, No. 3, 1831 (2019). MSC: 65M06 65M12 65M20 76R50 PDFBibTeX XMLCite \textit{G. Manzini} et al., J. Sci. Comput. 80, No. 3, 1805--1830 (2019; Zbl 1428.65013) Full Text: DOI
Vu-Huu, T.; Phung-Van, P.; Nguyen-Xuan, H.; Abdel Wahab, M. A polytree-based adaptive polygonal finite element method for topology optimization of fluid-submerged breakwater interaction. (English) Zbl 1427.76150 Comput. Math. Appl. 76, No. 5, 1198-1218 (2018). MSC: 76M10 74P15 74F10 74S05 65N30 76D05 PDFBibTeX XMLCite \textit{T. Vu-Huu} et al., Comput. Math. Appl. 76, No. 5, 1198--1218 (2018; Zbl 1427.76150) Full Text: DOI
Beltman, R.; Anthonissen, M. J. H.; Koren, B. Conservative polytopal mimetic discretization of the incompressible Navier-Stokes equations. (English) Zbl 1432.76153 J. Comput. Appl. Math. 340, 443-473 (2018). MSC: 76M10 65M60 35Q30 65M50 76D05 PDFBibTeX XMLCite \textit{R. Beltman} et al., J. Comput. Appl. Math. 340, 443--473 (2018; Zbl 1432.76153) Full Text: DOI
Vacca, Giuseppe An \(H^1\)-conforming virtual element for Darcy and Brinkman equations. (English) Zbl 1457.65218 Math. Models Methods Appl. Sci. 28, No. 1, 159-194 (2018). MSC: 65N30 65N12 65N15 76D07 76S05 35Q35 PDFBibTeX XMLCite \textit{G. Vacca}, Math. Models Methods Appl. Sci. 28, No. 1, 159--194 (2018; Zbl 1457.65218) Full Text: DOI arXiv
Liu, Xin; Li, Jian; Chen, Zhangxin A nonconforming virtual element method for the Stokes problem on general meshes. (English) Zbl 1439.76085 Comput. Methods Appl. Mech. Eng. 320, 694-711 (2017). MSC: 76M10 65N30 65N12 65N15 76D07 PDFBibTeX XMLCite \textit{X. Liu} et al., Comput. Methods Appl. Mech. Eng. 320, 694--711 (2017; Zbl 1439.76085) Full Text: DOI
Beirão da Veiga, Lourenço; Mora, David; Rivera, Gonzalo; Rodríguez, Rodolfo A virtual element method for the acoustic vibration problem. (English) Zbl 1397.76059 Numer. Math. 136, No. 3, 725-763 (2017). MSC: 76M10 65N30 65N25 70J30 76Q05 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Numer. Math. 136, No. 3, 725--763 (2017; Zbl 1397.76059) Full Text: DOI arXiv
Giani, S.; Houston, P. Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. (English) Zbl 1329.76170 J. Comput. Appl. Math. 270, 32-42 (2014). MSC: 76M10 65N30 65N15 65N50 76D05 PDFBibTeX XMLCite \textit{S. Giani} and \textit{P. Houston}, J. Comput. Appl. Math. 270, 32--42 (2014; Zbl 1329.76170) 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
Barbieri, Ettore; Meo, Michele A fast object-oriented MATLAB implementation of the reproducing kernel particle method. (English) Zbl 1398.74450 Comput. Mech. 49, No. 5, 581-602 (2012). MSC: 74S30 74S05 65N30 76M25 76N10 PDFBibTeX XMLCite \textit{E. Barbieri} and \textit{M. Meo}, Comput. Mech. 49, No. 5, 581--602 (2012; Zbl 1398.74450) Full Text: DOI
Beirão da Veiga, L.; Gyrya, V.; Lipnikov, K.; Manzini, G. Mimetic finite difference method for the Stokes problem on polygonal meshes. (English) Zbl 1172.76032 J. Comput. Phys. 228, No. 19, 7215-7232 (2009). MSC: 76M20 76D07 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., J. Comput. Phys. 228, No. 19, 7215--7232 (2009; Zbl 1172.76032) Full Text: DOI Link