Global error analysis of discontinuous Galerkin methods for systems of boundary value problems
Volume 33, Issue 4, pp 368--380
https://dx.doi.org/10.22436/jmcs.033.04.04
Publication Date: January 25, 2024
Submission Date: September 08, 2023
Revision Date: November 16, 2023
Accteptance Date: December 15, 2023
Authors
H. Temimi
- Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Hawally 32093, Kuwait.
Abstract
This paper introduces a novel approach for solving systems of boundary value problems (BVPs) by employing the recently developed Discontinuous Galerkin (DG) method, which removes the necessity for auxiliary variables. This marks the initial installment in a sequence of publications dedicated to exploring DG methods for solving partial differential equations (PDEs). In fact, through a systematic application of the DG method to each spatial variable within the PDE, employing the method of lines, we convert the initial problem into a system of ordinary differential equations (ODEs). In the current study, we developed a global error analysis of the DG method applied to systems of ODEs. Our analysis shows that using \(p\)-degree piecewise polynomials and \(h\)-mesh step size, the DG solutions achieve optimal \(O(h^{p+1})\) convergence rates in the \(\mathcal{L}^2\)-norm.
Share and Cite
ISRP Style
H. Temimi, Global error analysis of discontinuous Galerkin methods for systems of boundary value problems, Journal of Mathematics and Computer Science, 33 (2024), no. 4, 368--380
AMA Style
Temimi H., Global error analysis of discontinuous Galerkin methods for systems of boundary value problems. J Math Comput SCI-JM. (2024); 33(4):368--380
Chicago/Turabian Style
Temimi, H.. "Global error analysis of discontinuous Galerkin methods for systems of boundary value problems." Journal of Mathematics and Computer Science, 33, no. 4 (2024): 368--380
Keywords
- Discontinuous Galerkin
- superconvergence
- systems
- boundary value problems
- optimal rate
MSC
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