Stability and Error Estimates of a Novel Spectral Deferred Correction Time-Marching with Local Discontinuous Galerkin Methods for Parabolic Equations
In this paper, we discuss the stability and error estimates of the fully discrete schemes for parabolic equations, in which local discontinuous Galerkin methods with generalized alternating numerical fluxes and a novel spectral deferred correction method based on second-order time integration method...
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Published in | Journal of computational methods in applied mathematics Vol. 23; no. 1; pp. 277 - 296 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Minsk
De Gruyter
01.01.2023
Walter de Gruyter GmbH |
Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we discuss the stability and error estimates of the fully discrete schemes for parabolic equations, in which local discontinuous Galerkin methods with generalized alternating numerical fluxes and a novel spectral deferred correction method based on second-order time integration methods are adopted.
With the energy techniques, we obtain both the second- and fourth-order spectral deferred correction time-marching with local discontinuous Galerkin spatial discretization are unconditional stable.
The optimal error estimates for the corresponding fully discrete scheme are derived by the aid of the generalized Gauss–Radau projection.
We extend the analysis to problems with higher even-order derivatives.
Numerical examples are displayed to verify our theoretical results. |
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ISSN: | 1609-4840 1609-9389 |
DOI: | 10.1515/cmam-2022-0144 |