An L p- primal–dual weak Galerkin method for div–curl systems
References
[1]
Li J., Huang Y., Time-Domain Finite Element Methods for Maxwell’s Equations in Metamaterials, Springer, 2013.
[2]
Nicolaides R., Wu X., Covolume solutions of three-dimensional div–curl equations, SIAM J. Numer. Anal. 34 (1997) 2195–2203.
[3]
Bochev P.B., Peterson K., Siefert C.M., Analysis and computation of compatible least-squares methods for div–curl equations, SIAM J. Numer. Anal. 49 (2011) 159–181.
[4]
Bensow R., Larson M.G., Discontinuous least-squares finite element method for the div–curl problem, Numer. Math. 101 (2005) 601–617.
[5]
Bossavit A., Computational Electromagnetism, Academic Press, San Diego, 1998.
[6]
Nicolaides R.A., Direct discretization of planar div–curl problems, SIAM J. Numer. Anal. 29 (1992) 32–56.
[7]
Delcourte S., Domelevo K., Omnes P., A discrete duality finite volume approach to Hodge decomposition and div–curl problems on almost arbitrary two-dimensional meshes, SIAM J. Numer. Anal. 45 (2007) 1142–1174.
[8]
Copeland D.M., Gopalakrishnan J., Pasciak J.E., A mixed method for axisymmetric div–curl systems, Math. Comp. 77 (2008) 1941–1965.
[9]
Brezzi R., Buffa A., Innovative mimetic discretizations for electromagnetic problems, J. Comput. Appl. Math. 234 (2010) 1980–1987.
[10]
Lipnikov K., Manzini G., Brezzi F., Buffa A., The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes, J. Comput. Phys. 230 (2011) 305–328.
[11]
Wang C., Wang J., Discretization of div–curl systems by weak Galerkin finite element methods on polyhedral partitions, J. Sci. Comput. 68 (2016) 1144–1171.
[12]
Li J., Ye X., Zhang S., A weak Galerkin least-squares finite element method for div–curl systems, J. Comput. Phys. 363 (2018) 79–86.
[13]
Y. Liu, J. Wang, A primal–dual weak Galerkin method for div–curl systems with low-regularity solutions, arXiv preprint arXiv:2003.11795v2.
[14]
S. Cao, C. Wang, J. Wang, A new numerical method for div–curl Systems with Low Regularity Assumptions, arXiv preprint arXiv:2101.03466.
[15]
Cao W., Wang C., Applied Numerical Mathematics 162 (2021) 171–191.
[16]
Li D., Wang C., Wang J., Primal–dual weak galerkin finite element methods for linear convection equations in non-divergence form, Journal of Computational and Applied Mathematics 412 (2022) 114313.
[17]
Wang C., A new primal–dual weak Galerkin finite element method for ill-posed elliptic Cauchy problems, J. Comput. Appl. Math. (2019).
[18]
Wang C., Wang J., A primal–dual finite element method for first-order transport problems, J. Comput. Phys. 417 (2020).
[19]
Wang C., Wang J., A primal–dual weak galerkin finite element method for second order elliptic equations in non-divergence form, Math. Comp. 87 (2018) 515–545.
[20]
Wang C., Wang J., A primal–dual weak galerkin finite element method for Fokker–Planck type equations, SIAM J. Numer. Anal 58 (5) (2020) 2632–2661.
[21]
Wang C., Wang J., Primal–dual weak galerkin finite element methods for elliptic cauchy problems, Comput. Math. Appl. 79 (3) (2020) 746–763.
[22]
Wang C., Zikatanov L., Low regularity primal–dual weak galerkin finite element methods for convection–diffusion equations, Journal of Computational and Applied Mathematics 394 (2021) 113543.
[23]
Cao W., Wang C., Wang J., An L p-primal-dual weak galerkin method for convection-diffusion equations, Journal of Computational and Applied Mathematics 419 (2023) 114698.
[24]
Ciarlet P.G., The Finite Element Method for Elliptic Problems, North-Holland, 1978.
[25]
Girault V., Raviart P.-A., Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms, Springer-Verlag Berlin Heidelberg, 1986.
[26]
Wang J., Ye X., A weak galerkin mixed finite element method for second-order elliptic problems, Math. Comp. 83 (2014) 2101–2126.
[27]
Vogel C., Oman M., Iterative methods for total variation denoising, SIAM J. Sci. Comput. 17 (1996) 227–238.
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Published: 01 April 2023
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