Open Access
Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
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Page(s) | 881 - 926 | |
DOI | https://doi.org/10.1051/m2an/2024017 | |
Published online | 03 June 2024 |
- D. Adak, E. Natarajan and S. Kumar, Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes. Numer. Methods Partial Differ. Equ. 35 (2019) 222–245. [Google Scholar]
- B. Ahmad, A. Alsaedi, F. Brezzi, L.D. Marini and A. Russo, Equivalent projectors for virtual element methods. Comput. Math. Appl. 66 (2013) 376–391. [Google Scholar]
- V. Anaya, M. Bendahmane, D. Mora and M. Sepúlveda, A virtual element method for a nonlocal fitzhugh–nagumo model of cardiac electrophysiology. IMA J. Numer. Anal. 40 (2020) 1544–1576. [CrossRef] [MathSciNet] [Google Scholar]
- M. Arrutselvi and E. Natarajan, Virtual element stabilization for the system of time-dependent nonlinear convection-diffusion-reaction equations. Comput. Math. Appl. 142 (2023) 121–139. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirãao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini and A. Russo, Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23 (2012) 199–214. [Google Scholar]
- L. Beirãao da Veiga, F. Brezzi, L.D. Marini and A. Russo, The hitchhiker’s guide to the virtual element method. Math. Models Methods Appl. Sci. 24 (2014) 1541–1573. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirãao da Veiga, F. Brezzi, L.D. Marini and A. Russo, Virtual element method for general second-order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26 (2016) 729–750. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirãao da Veiga, C. Lovadina and A. Russo, Stability analysis for the virtual element method. Math. Models Methods Appl. Sci. 27 (2017) 2557–2594. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirãao da Veiga, A. Pichler and G. Vacca, A virtual element method for the miscible displacement of incompressible fluids in porous media. Comput. Methods Appl. Mech. Eng. 375 (2021) 113649. [CrossRef] [Google Scholar]
- S.C. Brenner and L.-Y. Sung, Virtual element methods on meshes with small edges or faces. Math. Models Methods Appl. Sci. 28 (2018) 1291–1336. [Google Scholar]
- A. Cangiani, P. Chatzipantelidis, G. Diwan and E.H. Georgoulis, Virtual element method for quasilinear elliptic problems. IMA J. Numer. Anal. 40 (2019) 2450–2472. [Google Scholar]
- J.R. Cannon and y. Lin, Non-classical h1 projection and galerkin methods for non-linear parabolic integro-differential equations. Calcolo 25 (1988) 187–201. [CrossRef] [MathSciNet] [Google Scholar]
- L. Chen and J. Huang, Some error analysis on virtual element methods. Calcolo 55 (2018) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Chen, Y. Huang and D. Yu, A two-grid method for expanded mixed finite-element solution of semilinear reaction–diffusion equations. Int. J. Numer. Methods Eng. 57 (2003) 193–209. [CrossRef] [Google Scholar]
- C.N. Dawson, Q. Du and T.F. Dupont, A finite difference domain decomposition algorithm for numerical solution of the heat equation. Math. comput. 57 (1991) 63–71. [CrossRef] [Google Scholar]
- L.C. Evans, Partial Differential Equations, Vol. 19. American Mathematical Society (2022). [Google Scholar]
- I. Farago, Finite element method for solving nonlinear parabolic equations. Comput. Math. Appl. 21 (1991) 59–69. [CrossRef] [MathSciNet] [Google Scholar]
- S.M.F. Garcia, Improved error estimates for mixed finite-element approximations for nonlinear parabolic equations: The continuous-time case. Numer. Methods Partial Differ. Equ. 10 (1994) 129–147. [Google Scholar]
- A.T. Hill and E. Süli, Approximation of the global attractor for the incompressible Navier–Stokes equations. IMA J. Numer. Anal. 20 (2000) 633–667. [CrossRef] [MathSciNet] [Google Scholar]
- M. Li, Cut-off error splitting technique for conservative nonconforming vem for n-coupled nonlinear schrödinger–boussinesq equations. J. Sci. Comput. 93 (2022) 86. [CrossRef] [Google Scholar]
- B. Li and W. Sun, Error analysis of linearized semi-implicit galerkin finite element methods for nonlinear parabolic equations. Int. J. Numer. Anal. Model. 10 (2013) 622–633. [MathSciNet] [Google Scholar]
- B. Li and W. Sun, Unconditional convergence and optimal error estimates of a galerkin-mixed fem for incompressible miscible flow in porous media. SIAM J. Numer. Anal. 51 (2013) 1959–1977. [CrossRef] [MathSciNet] [Google Scholar]
- B. Li and W. Sun, Unconditionally optimal error analysis of fully discrete galerkin methods for general nonlinear parabolic equations. Preprint: arXiv:1303.6410 (2013). [Google Scholar]
- D. Li and J. Wang, Unconditionally optimal error analysis of crank–nicolson galerkin fems for a strongly nonlinear parabolic system. J. Sci. Comput. 72 (2017) 892–915. [CrossRef] [MathSciNet] [Google Scholar]
- B. Li, H. Gao and W. Sun, Unconditionally optimal error estimates of a crank–nicolson galerkin method for the nonlinear thermistor equations. SIAM J. Numer. Anal. 52 (2014) 933–954. [CrossRef] [MathSciNet] [Google Scholar]
- M. Li, J. Zhao and Sh. Chen, Unconditional error analysis of vems for a generalized nonlinear schrodinger equation. J. Comput. Math. (2023). [Google Scholar]
- W. Liu, Y. Chen, Q. Gu and Y. Huang, Virtual element method for nonlinear sobolev equation on polygonal meshes. Numer. Algorithms (2023). [Google Scholar]
- M. Luskin, A galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. SIAM J. Numer. Anal. 16 (1979) 284–299. [CrossRef] [MathSciNet] [Google Scholar]
- H. Malchow, S.V. Petrovskii and E. Venturino, Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, and Simulation. CRC Press (2007). [CrossRef] [Google Scholar]
- J. Marshall, A. Adcroft, C. Hill, L. Perelman and C. Heisey, A finite-volume, incompressible navier stokes model for studies of the ocean on parallel computers. J. Geophys. Res. Oceans 102 (1997) 5753–5766. [CrossRef] [Google Scholar]
- A. Pinelli, I.Z. Naqavi, U. Piomelli and J. Favier, Immersed-boundary methods for general finite-difference and finite-volume navier–stokes solvers. J. Comput. Phys. 229 (2010) 9073–9091. [CrossRef] [MathSciNet] [Google Scholar]
- H.H. Rachford Jr., Two-level discrete-time galerkin approximations for second order nonlinear parabolic partial differential equations. SIAM J. Numer. Anal. 10 (1973) 1010–1026. [CrossRef] [MathSciNet] [Google Scholar]
- B. Rivière and M.F. Wheeler, A discontinuous galerkin method applied to nonlinear parabolic equations. In: Discontinuous Galerkin Methods: Theory, Computation and Applications. Springer (2000) 231–244. [CrossRef] [Google Scholar]
- C. Talischi, G.H. Paulino, A. Pereira and I.F. Menezes, PolyMesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct. Multidiscip. Optim. 45 (2012) 309–328. [CrossRef] [MathSciNet] [Google Scholar]
- V. Thomée, Galerkin Finite Element Methods for Parabolic Problems Second Edition, Vol. 1. Springer Science and Media (2006). [Google Scholar]
- G. Vacca and L. Beirãao da Veiga, Virtual element methods for parabolic problems on polygonal meshes. Numer. Methods Partial Differ. Equ. 31 (2015) 2110–2134. [CrossRef] [Google Scholar]
- N. Wang and M. Li, Unconditional error analysis of a linearized BDF2 virtual element method for nonlinear ginzburg–landau equation with variable time step. Commun. Nonlinear Sci. Numer. Simul. 116 (2023) 106889. [CrossRef] [Google Scholar]
- Y. Wang, Y. Chen and Y. Huang, A two-grid eulerian–lagrangian localized adjoint method to miscible displacement problems with dispersion term. Comput. Math. Appl. 80 (2020) 54–68. [CrossRef] [MathSciNet] [Google Scholar]
- H. Yi, Y. Chen, Y. Wang and Y. Huang, Optimal convergence analysis of a linearized second-order BDF-PPIFE method for semi-linear parabolic interface problems. Appl Math Comput. 438 (2023) 127581. [Google Scholar]
- Y. Yu, mVEM: MATLAB Programming for Virtual Element Methods (2019–2022). [Google Scholar]
- Y. Yu, mvem: A matlab software package for the virtual element methods. Preprint: arXiv:2204.01339 (2022). [Google Scholar]
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