The virtual element method for the time fractional convection diffusion reaction equation with non-smooth data

Computers & Mathematics with Applications - Tập 110 - Trang 1-18 - 2022
Yadong Zhang1,2, Minfu Feng1
1College of Mathematics, Sichuan University, 610065, Chengdu, China
2School of Science, Xuchang University, 461000, Xuchang, China

Tài liệu tham khảo

Podlubny, 1999 Kilbas, 2006 Liu, 2015 Baleanu, 2016, Fractional Calculus: Models and Numerical Methods, vol. 5 Liu, 2007, Stability and convergence of the difference methods for the space–time fractional advection–diffusion equation, Appl. Math. Comput., 191, 12, 10.1007/s40314-022-02142-4 Cui, 2015, Compact exponential scheme for the time fractional convection-diffusion reaction equation with variable coefficients, J. Comput. Phys., 280, 143, 10.1016/j.jcp.2014.09.012 Jiang, 2011, High-order finite element methods for time-fractional partial differential equations, J. Comput. Appl. Math., 235, 3285, 10.1016/j.cam.2011.01.011 Liu, 2017, Finite element algorithm based on high-order time approximation for time fractional convection-diffusion equation, J. Appl. Anal. Comput., 8, 229 Li, 2019, Nonconforming virtual element method for the time fractional reaction–subdiffusion equation with non-smooth data, J. Sci. Comput., 81, 1823, 10.1007/s10915-019-01064-4 Zhao, 2016, Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations, Appl. Math. Lett., 59, 38, 10.1016/j.aml.2016.03.005 Badr, 2018, Stability of a finite volume element method for the time-fractional advection-diffusion equation, Numer. Methods Partial Differ. Equ., 34, 1459, 10.1002/num.22243 Izadkhah, 2015, Gegenbauer spectral method for time-fractional convection–diffusion equations with variable coefficients, Math. Methods Appl. Sci., 38, 3183, 10.1002/mma.3289 Yu, 2017, A space-time spectral method for one-dimensional time fractional convection diffusion equations, Math. Methods Appl. Sci., 40, 2634, 10.1002/mma.4188 Bouharguane, 2020, The local discontinuous Galerkin method for convection-diffusion-fractional anti-diffusion equations, Appl. Numer. Math., 148, 61, 10.1016/j.apnum.2019.09.001 Ahmadinia, 2018, Analysis of local discontinuous Galerkin method for time–space fractional convection–diffusion equations, BIT Numer. Math., 58, 533, 10.1007/s10543-018-0697-x Wei, 2013, Analysis of a local discontinuous Galerkin method for time-fractional advection-diffusion equations, Int. J. Numer. Methods Heat Fluid Flow, 23, 634, 10.1108/09615531311323782 Tian, 2006, The flow analysis of fluids in fractal reservoir with the fractional derivative, J. Hydrodyn., 18, 287, 10.1016/S1001-6058(06)60005-X da Veiga, 2014, The Mimetic Finite Difference Method for Elliptic Problems, vol. 11 Cockburn, 2011, The hybridizable discontinuous Galerkin methods, 2749 Pietro, 2015, Hybrid high-order methods for variable-diffusion problems on general meshes, C. R. Math., 353, 31, 10.1016/j.crma.2014.10.013 Wang, 2014, A weak Galerkin mixed finite element method for second order elliptic problems, Math. Comput., 83, 2101, 10.1090/S0025-5718-2014-02852-4 Astaneh, 2017, High-order polygonal discontinuous Petrov–Galerkin (PolyDPG) methods using ultraweak formulations, Comput. Methods Appl. Mech. Eng., 332, 686, 10.1016/j.cma.2017.12.011 Fan, 2017, A novel unstructured mesh finite element method for solving the time-space fractional wave equation on a two-dimensional irregular convex domain, Fract. Calc. Appl. Anal., 20, 352, 10.1515/fca-2017-0019 Yang, 2020, An unstructured mesh finite difference/finite element method for the three-dimensional time-space fractional Bloch-Torrey equations on irregular domains, J. Comput. Phys., 408, 10.1016/j.jcp.2020.109284 Shi, 2019, An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain, Appl. Math. Model., 73, 615, 10.1016/j.apm.2019.04.023 Feng, 2020, An unstructured mesh control volume method for two-dimensional space fractional diffusion equations with variable coefficients on convex domains, J. Comput. Appl. Math., 364, 10.1016/j.cam.2019.06.035 da Veiga, 2014, The hitchhiker's guide to the virtual element method, Math. Models Methods Appl. Sci., 24, 1541, 10.1142/S021820251440003X Ahmad, 2013, Equivalent projectors for virtual element methods, Comput. Math. Appl., 66, 376, 10.1016/j.camwa.2013.05.015 Beir, 2013, Basic principles of virtual element methods, Math. Models Methods Appl. Sci., 23, 199, 10.1142/S0218202512500492 da Veiga, 2016, Virtual element implementation for general elliptic equations, Build. Bridges: Connect. Challenges Modern Approach. Numer. Partial Differ. Equ., 114, 39 Chen, 2018, Some error analysis on virtual element methods, Calcolo, 55, 1, 10.1007/s10092-018-0249-4 Chen, 2017, An interface-fitted mesh generator and virtual element methods for elliptic interface problems, J. Comput. Phys., 334, 327, 10.1016/j.jcp.2017.01.004 Vacca, 2015, Virtual element methods for parabolic problems on polygonal meshes: VEM for parabolic problems, Numer. Methods Partial Differ. Equ., 31, 2110, 10.1002/num.21982 Zhang, 2018, Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation, Appl. Math. Comput., 328, 1, 10.1016/j.cam.2017.12.045 Benedetto, 2016, Order preserving supg stabilization for the virtual element formulation of advection-diffusion problems, Comput. Methods Appl. Mech. Eng., 311, 18, 10.1016/j.cma.2016.07.043 Brezzi, 2014, Basic principles of mixed virtual element methods, Math. Model. Numer. Anal., 48, 1227, 10.1051/m2an/2013138 Lovadina, 2018, Mixed virtual element methods for elasticity problems, 25 da Veiga, 2016, Mixed virtual element methods for general second order elliptic problems on polygonal meshes, Math. Model. Numer. Anal., 50, 727, 10.1051/m2an/2015067 Zhang, 2019, Mixed virtual element methods for elastodynamics with weak symmetry, J. Comput. Appl. Math., 353, 49, 10.1016/j.cam.2018.12.020 de Dios, 2016, The nonconforming virtual element method, Math. Model. Numer. Anal., 50, 879, 10.1051/m2an/2015090 Cangiani, 2016, Conforming and nonconforming virtual element methods for elliptic problems, IMA J. Numer. Anal., 37, 1317 Cangiani, 2016, The nonconforming virtual element method for the stokes equations, SIAM J. Numer. Anal., 54, 3411, 10.1137/15M1049531 Zhao, 2019, The nonconforming virtual element method for parabolic problems, Appl. Numer. Math., 143, 97, 10.1016/j.apnum.2019.04.002 Veiga, 2016, H(div) and h(curl)-conforming virtual element methods, Numer. Math., 133, 303 Brezzi, 2014, Virtual element and discontinuous Galerkin methods, 209 Chen, 2021, Blow-up of error estimates in time-fractional initial-boundary value problems, IMA J. Numer. Anal., 41, 974, 10.1093/imanum/draa015 Liao, 2012, A compact high-order finite difference method for unsteady convection-diffusion equation, Int. J. Comput. Methods Eng. Sci. Mech., 13, 135, 10.1080/15502287.2012.660227 Zhai, 2014, An unconditionally stable compact ADI method for three-dimensional time-fractional convection–diffusion equation, J. Comput. Phys., 269, 138, 10.1016/j.jcp.2014.03.020 Stynes, 2017, Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation, SIAM J. Numer. Anal., 55, 1057, 10.1137/16M1082329 Sakamoto, 2011, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, J. Math. Anal. Appl., 382, 426, 10.1016/j.jmaa.2011.04.058 Kopteva, 2019, Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions, Math. Comput., 88, 2135, 10.1090/mcom/3410 Alikhanov, 2010, A priori estimates for solutions of boundary value problems for fractional-order equations, Differ. Equ., 46, 660, 10.1134/S0012266110050058 Chen, 2019, Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem, J. Sci. Comput., 79, 624, 10.1007/s10915-018-0863-y