Bertrand, Fleurianne Novel Raviart-Thomas basis functions on anisotropic finite elements. (English) Zbl 1527.65124 Comput. Methods Appl. Math. 23, No. 4, 831-847 (2023). MSC: 65N30 PDFBibTeX XMLCite \textit{F. Bertrand}, Comput. Methods Appl. Math. 23, No. 4, 831--847 (2023; Zbl 1527.65124) Full Text: DOI
Cao, Shuhao; Chen, Long; Guo, Ruchi Immersed virtual element methods for electromagnetic interface problems in three dimensions. (English) Zbl 1514.65164 Math. Models Methods Appl. Sci. 33, No. 3, 455-503 (2023). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{S. Cao} et al., Math. Models Methods Appl. Sci. 33, No. 3, 455--503 (2023; Zbl 1514.65164) Full Text: DOI arXiv
Ishizaka, Hiroki Anisotropic Raviart-Thomas interpolation error estimates using a new geometric parameter. (English) Zbl 1506.65215 Calcolo 59, No. 4, Paper No. 50, 27 p. (2022). MSC: 65N30 65D05 65N15 PDFBibTeX XMLCite \textit{H. Ishizaka}, Calcolo 59, No. 4, Paper No. 50, 27 p. (2022; Zbl 1506.65215) Full Text: DOI arXiv
Cao, Shuhao; Chen, Long; Guo, Ruchi A virtual finite element method for two-dimensional Maxwell interface problems with a background unfitted mesh. (English) Zbl 1478.65117 Math. Models Methods Appl. Sci. 31, No. 14, 2907-2936 (2021). MSC: 65N30 65N12 65N15 46E35 PDFBibTeX XMLCite \textit{S. Cao} et al., Math. Models Methods Appl. Sci. 31, No. 14, 2907--2936 (2021; Zbl 1478.65117) Full Text: DOI arXiv
Khademi, Ali; Korotov, Sergey; Vatne, Jon Eivind On mesh regularity conditions for simplicial finite elements. (English) Zbl 1475.65192 Vermolen, Fred J. (ed.) et al., Numerical mathematics and advanced applications. ENUMATH 2019. Proceedings of the European conference, Egmond aan Zee, The Netherlands, September 30 – October 4, 2019. Cham: Springer. Lect. Notes Comput. Sci. Eng. 139, 633-640 (2021). MSC: 65N30 PDFBibTeX XMLCite \textit{A. Khademi} et al., Lect. Notes Comput. Sci. Eng. 139, 633--640 (2021; Zbl 1475.65192) Full Text: DOI
Cejas, María E.; Durán, Ricardo G.; Prieto, Mariana I. Mixed methods for degenerate elliptic problems and application to fractional Laplacian. (English) Zbl 1477.65200 ESAIM, Math. Model. Numer. Anal. 55, Suppl., 993-1019 (2021). MSC: 65N30 35J70 26A33 35R11 PDFBibTeX XMLCite \textit{M. E. Cejas} et al., ESAIM, Math. Model. Numer. Anal. 55, 993--1019 (2021; Zbl 1477.65200) Full Text: DOI arXiv
Ishizaka, Hiroki; Kobayashi, Kenta; Tsuchiya, Takuya Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition. (English) Zbl 1477.65223 Japan J. Ind. Appl. Math. 38, No. 2, 645-675 (2021). MSC: 65N30 65N50 65N12 65N15 65D05 35J05 PDFBibTeX XMLCite \textit{H. Ishizaka} et al., Japan J. Ind. Appl. Math. 38, No. 2, 645--675 (2021; Zbl 1477.65223) Full Text: DOI arXiv
Apel, Thomas; Kempf, Volker Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading. (English) Zbl 1477.65187 Calcolo 58, No. 2, Paper No. 15, 20 p. (2021). MSC: 65N30 65N50 65N15 65N12 76M10 76D07 35Q35 PDFBibTeX XMLCite \textit{T. Apel} and \textit{V. Kempf}, Calcolo 58, No. 2, Paper No. 15, 20 p. (2021; Zbl 1477.65187) Full Text: DOI arXiv
Ishizaka, Hiroki; Kobayashi, Kenta; Tsuchiya, Takuya General theory of interpolation error estimates on anisotropic meshes. (English) Zbl 1467.65009 Japan J. Ind. Appl. Math. 38, No. 1, 163-191 (2021); correction ibid. 40, No. 2, 1355-1356 (2023). MSC: 65D05 65N30 PDFBibTeX XMLCite \textit{H. Ishizaka} et al., Japan J. Ind. Appl. Math. 38, No. 1, 163--191 (2021; Zbl 1467.65009) Full Text: DOI arXiv
Apel, Thomas; Kempf, Volker Brezzi-Douglas-Marini interpolation of any order on anisotropic triangles and tetrahedra. (English) Zbl 07210678 SIAM J. Numer. Anal. 58, No. 3, 1696-1718 (2020). MSC: 65D05 65N30 PDFBibTeX XMLCite \textit{T. Apel} and \textit{V. Kempf}, SIAM J. Numer. Anal. 58, No. 3, 1696--1718 (2020; Zbl 07210678) Full Text: DOI arXiv
Dubois, Francois; Greff, Isabelle; Pierre, Charles Raviart-Thomas finite elements of Petrov-Galerkin type. (English) Zbl 1427.65335 ESAIM, Math. Model. Numer. Anal. 53, No. 5, 1553-1576 (2019). MSC: 65N08 65N12 65N30 35J25 35J05 PDFBibTeX XMLCite \textit{F. Dubois} et al., ESAIM, Math. Model. Numer. Anal. 53, No. 5, 1553--1576 (2019; Zbl 1427.65335) Full Text: DOI arXiv
Monzón, Gabriel Anisotropic interpolation error estimate for arbitrary quadrilateral isoparametric elements. (English) Zbl 1426.65165 Numer. Math. 143, No. 2, 315-338 (2019). MSC: 65N15 65N30 PDFBibTeX XMLCite \textit{G. Monzón}, Numer. Math. 143, No. 2, 315--338 (2019; Zbl 1426.65165) Full Text: DOI arXiv
Verfürth, Rüdiger; Zanotti, Pietro A quasi-optimal Crouzeix-Raviart discretization of the Stokes equations. (English) Zbl 1422.65416 SIAM J. Numer. Anal. 57, No. 3, 1082-1099 (2019). MSC: 65N30 65N15 65J10 76D07 35Q35 PDFBibTeX XMLCite \textit{R. Verfürth} and \textit{P. Zanotti}, SIAM J. Numer. Anal. 57, No. 3, 1082--1099 (2019; Zbl 1422.65416) Full Text: DOI arXiv
John, Volker; Knobloch, Petr; Novo, Julia Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story? (English) Zbl 07704544 Comput. Vis. Sci. 19, No. 5-6, 47-63 (2018). MSC: 65Nxx PDFBibTeX XMLCite \textit{V. John} et al., Comput. Vis. Sci. 19, No. 5--6, 47--63 (2018; Zbl 07704544) Full Text: DOI
Baĭdakova, N. V. On Jamet’s estimates for the finite element method with interpolation at uniform nodes of a simplex. (Russian, English) Zbl 1399.65312 Mat. Tr. 20, No. 1, 43-74 (2017); translation in Sib. Adv. Math. 28, No. 1, 1-22 (2018). MSC: 65N15 65N30 65D05 PDFBibTeX XMLCite \textit{N. V. Baĭdakova}, Mat. Tr. 20, No. 1, 43--74 (2017; Zbl 1399.65312); translation in Sib. Adv. Math. 28, No. 1, 1--22 (2018) Full Text: DOI
Chen, Long; Wei, Huayi; Wen, Min An interface-fitted mesh generator and virtual element methods for elliptic interface problems. (English) Zbl 1380.65400 J. Comput. Phys. 334, 327-348 (2017). MSC: 65N50 65N30 35R05 PDFBibTeX XMLCite \textit{L. Chen} et al., J. Comput. Phys. 334, 327--348 (2017; Zbl 1380.65400) Full Text: DOI
Acosta, Gabriel; Monzón, Gabriel The minimal angle condition for quadrilateral finite elements of arbitrary degree. (English) Zbl 1357.65236 J. Comput. Appl. Math. 317, 218-234 (2017). MSC: 65N15 65N30 PDFBibTeX XMLCite \textit{G. Acosta} and \textit{G. Monzón}, J. Comput. Appl. Math. 317, 218--234 (2017; Zbl 1357.65236) Full Text: DOI Link
Bespalov, A.; Nicaise, Serge A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces. (English) Zbl 1443.65399 Comput. Math. Appl. 71, No. 8, 1636-1644 (2016). MSC: 65N38 65N15 78M15 PDFBibTeX XMLCite \textit{A. Bespalov} and \textit{S. Nicaise}, Comput. Math. Appl. 71, No. 8, 1636--1644 (2016; Zbl 1443.65399) Full Text: DOI
Auricchio, Ferdinando; Lefieux, Adrien; Reali, Alessandro On the use of anisotropic triangles with mixed finite elements: application to an “immersed” approach for incompressible flow problems. (English) Zbl 1354.76095 Schröder, Jörg (ed.) et al., Advanced finite element technologies. Cham: Springer (ISBN 978-3-319-31923-0/hbk; 978-3-319-31925-4/ebook). CISM Courses and Lectures 566, 195-236 (2016). MSC: 76M10 76D07 PDFBibTeX XMLCite \textit{F. Auricchio} et al., in: Advanced finite element technologies. Cham: Springer. 195--236 (2016; Zbl 1354.76095) Full Text: DOI
Ferreira, José A.; Pinto, Luís An integro-differential model for non-Fickian tracer transport in porous media: validation and numerical simulation. (English) Zbl 1398.76216 Math. Methods Appl. Sci. 39, No. 16, 4736-4749 (2016). MSC: 76S05 76M10 65R20 45K05 65M60 65N30 PDFBibTeX XMLCite \textit{J. A. Ferreira} and \textit{L. Pinto}, Math. Methods Appl. Sci. 39, No. 16, 4736--4749 (2016; Zbl 1398.76216) Full Text: DOI Link
Xu, Jinchao; Zhang, Shuo Optimal finite element methods for interface problems. (English) Zbl 1339.65224 Dickopf, Thomas (ed.) et al., Domain decomposition methods in science and engineering XXII. Proceedings of the 22nd international conference on domain decomposition methods, Lugano, Switzerland, September 16–20, 2013. Cham: Springer (ISBN 978-3-319-18826-3/hbk; 978-3-319-18827-0/ebook). Lecture Notes in Computational Science and Engineering 104, 77-91 (2016). MSC: 65N30 PDFBibTeX XMLCite \textit{J. Xu} and \textit{S. Zhang}, Lect. Notes Comput. Sci. Eng. 104, 77--91 (2016; Zbl 1339.65224) Full Text: DOI
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
Linke, A.; Merdon, C. Guaranteed energy error estimators for a modified robust Crouzeix-Raviart Stokes element. (English) Zbl 1330.76074 J. Sci. Comput. 64, No. 2, 541-558 (2015). MSC: 76M10 65N30 65N15 35Q30 PDFBibTeX XMLCite \textit{A. Linke} and \textit{C. Merdon}, J. Sci. Comput. 64, No. 2, 541--558 (2015; Zbl 1330.76074) Full Text: DOI
Linke, Alexander On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime. (English) Zbl 1295.76007 Comput. Methods Appl. Mech. Eng. 268, 782-800 (2014). MSC: 76D05 65N30 76M10 PDFBibTeX XMLCite \textit{A. Linke}, Comput. Methods Appl. Mech. Eng. 268, 782--800 (2014; Zbl 1295.76007) Full Text: DOI
Stynes, Martin Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements. (English) Zbl 1300.65079 Math. Comput. 83, No. 290, 2675-2689 (2014). Reviewer: Marius Ghergu (Dublin) MSC: 65N15 65N30 65N12 PDFBibTeX XMLCite \textit{M. Stynes}, Math. Comput. 83, No. 290, 2675--2689 (2014; Zbl 1300.65079) Full Text: DOI
Acosta, Gabriel; Armentano, María G. Finite element approximations in a non-Lipschitz domain. II. (English) Zbl 1329.65266 Math. Comput. 80, No. 276, 1949-1978 (2011). MSC: 65N30 65N15 46E35 PDFBibTeX XMLCite \textit{G. Acosta} and \textit{M. G. Armentano}, Math. Comput. 80, No. 276, 1949--1978 (2011; Zbl 1329.65266) Full Text: DOI
Chen, Shaochun; Zheng, Yanjun; Mao, Shipeng Anisotropic error bounds of Lagrange interpolation with any order in two and three dimensions. (English) Zbl 1222.41004 Appl. Math. Comput. 217, No. 22, 9313-9321 (2011). Reviewer: Antonio López-Carmona (Granada) MSC: 41A05 65D05 PDFBibTeX XMLCite \textit{S. Chen} et al., Appl. Math. Comput. 217, No. 22, 9313--9321 (2011; Zbl 1222.41004) Full Text: DOI
Acosta, Gabriel; Apel, Thomas; Durán, Ricardo G.; Lombardi, Ariel L. Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra. (English) Zbl 1223.65086 Math. Comput. 80, No. 273, 141-163 (2011). Reviewer: Laura Iulia Aniţa (Iaşi) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{G. Acosta} et al., Math. Comput. 80, No. 273, 141--163 (2011; Zbl 1223.65086) Full Text: DOI arXiv
Duan, Huo-Yuan; Tan, Roger C. E. On the Poincaré-Friedrichs inequality for piecewise \(H^{1}\) functions in anisotropic discontinuous Galerkin finite element methods. (English) Zbl 1208.26023 Math. Comput. 80, No. 273, 119-140 (2011). MSC: 26D10 46E35 65M60 65N30 PDFBibTeX XMLCite \textit{H.-Y. Duan} and \textit{R. C. E. Tan}, Math. Comput. 80, No. 273, 119--140 (2011; Zbl 1208.26023) Full Text: DOI
Morrison, N. F.; Rallison, J. M. Transient 3D flow of polymer solutions: a Lagrangian computational method. (English) Zbl 1274.76049 J. Non-Newton. Fluid Mech. 165, No. 19-20, 1241-1257 (2010). MSC: 76A05 76M10 PDFBibTeX XMLCite \textit{N. F. Morrison} and \textit{J. M. Rallison}, J. Non-Newton. Fluid Mech. 165, No. 19--20, 1241--1257 (2010; Zbl 1274.76049) Full Text: DOI Link
Blasco, Jordi An anisotropic GLS-stabilized finite element method for incompressible flow problems. (English) Zbl 1194.76103 Comput. Methods Appl. Mech. Eng. 197, No. 45-48, 3712-3723 (2008). MSC: 76M10 76D05 PDFBibTeX XMLCite \textit{J. Blasco}, Comput. Methods Appl. Mech. Eng. 197, No. 45--48, 3712--3723 (2008; Zbl 1194.76103) Full Text: DOI
Chen, ShaoChun; Xiao, LiuChao Interpolation theory of anisotropic finite elements and applications. (English) Zbl 1165.65067 Sci. China, Ser. A 51, No. 8, 1361-1375 (2008). Reviewer: Abdallah Bradji (Tebessa) MSC: 65N15 65N30 65D05 35J25 PDFBibTeX XMLCite \textit{S. Chen} and \textit{L. Xiao}, Sci. China, Ser. A 51, No. 8, 1361--1375 (2008; Zbl 1165.65067) Full Text: DOI
Shi, Dongyang; Wang, Caixia A locking-free anisotropic nonconforming rectangular finite element approximation for the planar elasticity problem. (English) Zbl 1150.74094 Appl. Math., Ser. B (Engl. Ed.) 23, No. 1, 9-18 (2008). MSC: 74S05 65N30 PDFBibTeX XMLCite \textit{D. Shi} and \textit{C. Wang}, Appl. Math., Ser. B (Engl. Ed.) 23, No. 1, 9--18 (2008; Zbl 1150.74094) Full Text: DOI
Nicaise, S.; Soualem, N. A posteriori error estimates for a nonconforming finite element discretization of the time-dependent Stokes problem. II: Analysis of the spatial estimator. (English) Zbl 1213.76121 J. Numer. Math. 15, No. 3, 209-231 (2007). MSC: 76M10 76D07 65M15 65M60 PDFBibTeX XMLCite \textit{S. Nicaise} and \textit{N. Soualem}, J. Numer. Math. 15, No. 3, 209--231 (2007; Zbl 1213.76121) Full Text: DOI
Blasco, Jordi An anisotropic pressure-stabilized finite element method for incompressible flow problems. (English) Zbl 1121.76031 Comput. Math. Appl. 53, No. 6, 895-909 (2007). MSC: 76M10 76D05 PDFBibTeX XMLCite \textit{J. Blasco}, Comput. Math. Appl. 53, No. 6, 895--909 (2007; Zbl 1121.76031) Full Text: DOI
Mao, Shipeng; Shi, Zhongci Nonconforming rotated \(Q_1\) element on non-tensor product anisotropic meshes. (English) Zbl 1112.65121 Sci. China, Ser. A 49, No. 10, 1363-1375 (2006). Reviewer: H. P. Dikshit (New Delhi) MSC: 65N30 65N15 35J25 65N50 PDFBibTeX XMLCite \textit{S. Mao} and \textit{Z. Shi}, Sci. China, Ser. A 49, No. 10, 1363--1375 (2006; Zbl 1112.65121) Full Text: DOI
Acosta, Gabriel; Monzón, Gabriel Interpolation error estimates in \(W^{1,p}\) for degenerate \(Q_1\) isoparametric elements. (English) Zbl 1120.65116 Numer. Math. 104, No. 2, 129-150 (2006). Reviewer: Petr Necesal (Plzen) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{G. Acosta} and \textit{G. Monzón}, Numer. Math. 104, No. 2, 129--150 (2006; Zbl 1120.65116) Full Text: DOI
Mao, Shipeng; Chen, Shaochun; Sun, Huixia A quadrilateral, anisotropic, superconvergent, nonconforming double set parameter element. (English) Zbl 1094.65120 Appl. Numer. Math. 56, No. 7, 937-961 (2006). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{S. Mao} et al., Appl. Numer. Math. 56, No. 7, 937--961 (2006; Zbl 1094.65120) Full Text: DOI
Domelevo, Komla; Omnes, Pascal A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. (English) Zbl 1086.65108 ESAIM, Math. Model. Numer. Anal. 39, No. 6, 1203-1249 (2005). Reviewer: Erwin Schechter (Moers) MSC: 65N30 65N12 35J05 65N50 65N15 PDFBibTeX XMLCite \textit{K. Domelevo} and \textit{P. Omnes}, ESAIM, Math. Model. Numer. Anal. 39, No. 6, 1203--1249 (2005; Zbl 1086.65108) Full Text: DOI Numdam EuDML
Nicaise, Serge; Soualem, Nadir A posteriori error estimates for a nonconforming finite element discretization of the heat equation. (English) Zbl 1078.65079 ESAIM, Math. Model. Numer. Anal. 39, No. 2, 319-348 (2005). Reviewer: Nicolae Pop (Baia Mare) MSC: 65M15 65M60 65M06 35K05 PDFBibTeX XMLCite \textit{S. Nicaise} and \textit{N. Soualem}, ESAIM, Math. Model. Numer. Anal. 39, No. 2, 319--348 (2005; Zbl 1078.65079) Full Text: DOI Numdam EuDML
Buffa, A.; Costabel, M.; Dauge, M. Algebraic convergence for anisotropic edge elements in polyhedral domains. (English) Zbl 1116.78020 Numer. Math. 101, No. 1, 29-65 (2005). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 78M10 65N15 65N30 65N25 PDFBibTeX XMLCite \textit{A. Buffa} et al., Numer. Math. 101, No. 1, 29--65 (2005; Zbl 1116.78020) Full Text: DOI
Apel, T.; Nicaise, S. The inf-sup condition for low order elements on anisotropic meshes. (English) Zbl 1108.65117 Calcolo 41, No. 2, 89-113 (2004). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N30 35Q30 PDFBibTeX XMLCite \textit{T. Apel} and \textit{S. Nicaise}, Calcolo 41, No. 2, 89--113 (2004; Zbl 1108.65117) Full Text: DOI
Randrianarivony, Maharavo Anisotropic finite elements for the Stokes problem: a posteriori error estimator and adaptive mesh. (English) Zbl 1060.65120 J. Comput. Appl. Math. 169, No. 2, 255-275 (2004). Reviewer: Michel Bernadou (Paris La Defense) MSC: 65N15 65N30 65N50 35Q30 35J25 74S05 PDFBibTeX XMLCite \textit{M. Randrianarivony}, J. Comput. Appl. Math. 169, No. 2, 255--275 (2004; Zbl 1060.65120) Full Text: DOI
Chen, Shaochun; Zhao, Yongcheng; Shi, Dongyang Anisotropic interpolations with application to nonconforming elements. (English) Zbl 1057.65082 Appl. Numer. Math. 49, No. 2, 135-152 (2004). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 65N30 35J25 PDFBibTeX XMLCite \textit{S. Chen} et al., Appl. Numer. Math. 49, No. 2, 135--152 (2004; Zbl 1057.65082) Full Text: DOI
Apel, Thomas; Randrianarivony, H. Maharavo Stability of discretizations of the Stokes problem on anisotropic meshes. (English) Zbl 1205.76072 Math. Comput. Simul. 61, No. 3-6, 437-447 (2003). MSC: 76D05 76M25 PDFBibTeX XMLCite \textit{T. Apel} and \textit{H. M. Randrianarivony}, Math. Comput. Simul. 61, No. 3--6, 437--447 (2003; Zbl 1205.76072) Full Text: DOI
Farhloul, Mohamed; Nicaise, Serge; Paquet, Luc Some mixed finite element methods on anisotropic meshes. (English) Zbl 0990.65129 M2AN, Math. Model. Numer. Anal. 35, No. 5, 907-920 (2001). Reviewer: Karel Najzar (Praha) MSC: 65N30 65N50 65N15 35J05 PDFBibTeX XMLCite \textit{M. Farhloul} et al., M2AN, Math. Model. Numer. Anal. 35, No. 5, 907--920 (2001; Zbl 0990.65129) Full Text: DOI Numdam EuDML
Acosta, Gabriel Lagrange and average interpolation over 3D anisotropic elements. (English) Zbl 0991.41004 J. Comput. Appl. Math. 135, No. 1, 91-109 (2001). Reviewer: Hang Tong Lau (St.Laurent/Quebec) MSC: 41A05 PDFBibTeX XMLCite \textit{G. Acosta}, J. Comput. Appl. Math. 135, No. 1, 91--109 (2001; Zbl 0991.41004) Full Text: DOI