Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-new-family-of-expanded-mixed-finite-element-methods-for-reaction-kyBqT8cetH
References (32)
-
Na Li, P. Lin, Fuzheng Gao (2019)
An expanded mixed finite element method for two-dimensional Sobolev equationsJ. Comput. Appl. Math., 348
-
T. Arbogast, M. Wheeler, I. Yotov (1997)
Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite DifferencesSIAM Journal on Numerical Analysis, 34
-
Jiansong Zhang, Danping Yang (2009)
A splitting positive definite mixed element method for second‐order hyperbolic equationsNumerical Methods for Partial Differential Equations, 25
-
PA Raviart (1977)
292 -
F Brezzi (1985)
217Numer. Math., 88
-
Yuezhi Zhang, Jiansong Zhang (2017)
The splitting mixed element method for parabolic equation and its application in chemotaxis modelAppl. Math. Comput., 313
-
F. Hecht (2012)
New development in freefem++, 20
-
R. Falk, J. Osborn (1980)
Error estimates for mixed methods, 14
-
Jiansong Zhang, Hui Guo (2012)
A split least-squares characteristic mixed element method for nonlinear nonstationary convection–diffusion problemInternational Journal of Computer Mathematics, 89
-
Z Liu (2005)
Expanded mixed finite element methods for the 2nd order parabolic problemsJ. Shandong Normal Univ., 20
-
PA Raviart, TM Thomas, I Galligam, E Magenes (1977)
A mixed finite element method for second order elliptic problemsMathematical Aspects of FEM
-
Keyan Wang, Qi-sheng Wang (2019)
Expanded mixed finite element method for second order hyperbolic equationsComput. Math. Appl., 78
-
A. Ibragimov, T. Kieu (2014)
An expanded mixed finite element method for generalized Forchheimer flows in porous mediaComput. Math. Appl., 72
-
F. Brezzi (1974)
On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers, 8
-
Zhangxin Chen (1998)
Expanded mixed finite element methods for quasilinear second order elliptic problems, IIMathematical Modelling and Numerical Analysis, 32
-
F. Brezzi, J. Douglas, M. Fortin, D. Marini (1987)
E cient rectangular mixed fi-nite elements in two and three space variablesJournal of Multivariate Analysis
-
Jiansong Zhang, Danping Yang, S. Shen, Jiang Zhu (2014)
A new MMOCAA-MFE method for compressible miscible displacement in porous mediaApplied Numerical Mathematics, 80
-
Y Liu (2008)
234Numer. Math. J. Chin. Univ., 30
-
Y Zhang (2017)
287Appl. Math. Comput., 313
-
J. Nédélec (1980)
Mixed finite elements in ℝ3Numerische Mathematik, 35
-
Y Liu, H Li, Z Wen (2008)
Expanded mixed finite element method for a kind of two-order linear parabolic differential equationNumer. Math. J. Chin. Univ., 30
-
Zhangxin Chen (1998)
Expanded mixed finite element methods for linear second-order elliptic problems, IMathematical Modelling and Numerical Analysis, 32
-
D Yang (2001)
229Numer. Methods Partial Differ. Equ., 17
-
V Thomee (1997)
10.1007/978-3-662-03359-3Galerkin Finite Element Methods for Parabolic Problems
-
I. Babuska (1971)
Error-bounds for finite element methodNumerische Mathematik, 16
-
F Brezzi (1974)
129ESAIM Math. Model. Numer. Anal., 8
-
Huailing Song, Lijian Jiang, Gaojie Chen (2014)
Convergence analysis of hybrid expanded mixed finite element method for elliptic equationsComput. Math. Appl., 68
-
H. Rui, Sang Kim, Seokchan Kim (2009)
Split least-squares finite element methods for linear and nonlinear parabolic problemsJournal of Computational and Applied Mathematics, 223
-
F. Brezzi, J. Douglas, R. Durán, M. Fortin (1987)
Mixed finite elements for second order elliptic problems in three variablesNumerische Mathematik, 51
-
Z Liu (2005)
1J. Shandong Normal Univ., 20
-
H. Rui, Seokchan Kim, Sang Kim (2007)
A remark on least-squares mixed element methods for reaction-diffusion problemsJournal of Computational and Applied Mathematics, 202
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © Korean Society for Informatics and Computational Applied Mathematics 2021
- ISSN
- 1598-5865
- eISSN
- 1865-2085
- DOI
- 10.1007/s12190-021-01634-6
- Publisher site
- See Article on Publisher Site
Abstract
A new family of expanded mixed finite element methods is constructed for solving the reaction–diffusion equations. Compared with the traditional expanded mixed element methods, the new methods result into splitting systems and the coefficient matrixes are symmetric positive definite. The uniqueness and stability of the proposed algorithms are considered, and the corresponding error estimates are derived. Finally, some numerical examples are presented to verify the effectiveness of the proposed algorithms.
Journal
Journal of Applied Mathematics and Computing – Springer Journals
Published: Aug 1, 2022
Keywords: Expanded mixed element; Splitting system; Convergence analysis; Reaction–diffusion equations; 65M15; 65M60; 65N12; 65N15; 65N30