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Stability analysis and error estimates of implicit Runge-Kutta local discontinuous Galerkin methods for linear bi-harmonic equation.
- Source :
-
Computers & Mathematics with Applications . Nov2023, Vol. 149, p211-220. 10p. - Publication Year :
- 2023
-
Abstract
- In this paper, stability analysis and error estimates of a fully discrete local discontinuous Galerkin method for solving the linear bi-harmonic equation are carried out, where the time discretization is treated by a strong-stability-preserving implicit Runge-Kutta scheme. Based on the generalized alternating numerical fluxes, the relationship between the numerical solution and the inner product of the auxiliary solution is established, which plays a key role in obtaining the unconditional stability of the fully discrete local discontinuous Galerkin methods. By carefully introducing reference functions and generalized Gauss-Radau projection, the optimal error estimates are obtained. Numerical experiments are given to demonstrate the stability and accuracy of the fully discrete scheme for the linear bi-harmonic equation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BIHARMONIC equations
*GALERKIN methods
*LINEAR equations
*CRANK-nicolson method
Subjects
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 149
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 172976881
- Full Text :
- https://doi.org/10.1016/j.camwa.2023.09.022