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Application of spectral element method for solving Sobolev equations with error estimation.
- Source :
-
Applied Numerical Mathematics . Dec2020, Vol. 158, p439-462. 24p. - Publication Year :
- 2020
-
Abstract
- This paper is dedicated to numerically solving the Sobolev equations that have several applications in physics and mechanical engineering. First, the temporal derivative is discretized by the Crank-Nicolson finite difference technique to obtain a semi-discrete scheme in the temporal direction. Afterward, the stability and convergence analysis of the time semi-discrete scheme are proven by applying the energy method. It also implies that the convergence order in the temporal direction is O (d t 2). Second, a fully discrete formula has been acquired by discretizing the spatial derivatives via Legendre spectral element method (LSEM). This method applies the Lagrange polynomial based on the Gauss-Legendre-Lobatto (GLL) points. Moreover, an error estimation is given for the obtained fully discrete scheme. Eventually, the two-dimensional Sobolev equations are solved by using the proposed procedure. The accuracy and efficiency of the mentioned procedure are demonstrated by several numerical examples. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SPECTRAL element method
*EQUATIONS
*FINITE differences
*APPLIED mechanics
Subjects
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 158
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 145628403
- Full Text :
- https://doi.org/10.1016/j.apnum.2020.08.010