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Two-grid Raviart-Thomas mixed finite element methods combined with Crank-Nicolson scheme for a class of nonlinear parabolic equations.
- Source :
-
Advances in Computational Mathematics . Apr2020, Vol. 46 Issue 2, p1-24. 24p. - Publication Year :
- 2020
-
Abstract
- In this paper, we discuss a priori error estimates of two-grid mixed finite element methods for a class of nonlinear parabolic equations. The lowest order Raviart-Thomas mixed finite element and Crank-Nicolson scheme are used for the spatial and temporal discretization. First, we derive the optimal a priori error estimates for all variables. Second, we present a two-grid scheme and analyze its convergence. It is shown that if the two mesh sizes satisfy h = H2, then the two-grid method achieves the same convergence property as the Raviart-Thomas mixed finite element method. Finally, we give a numerical example to verify the theoretical results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10197168
- Volume :
- 46
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Advances in Computational Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 142174413
- Full Text :
- https://doi.org/10.1007/s10444-020-09777-z