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Mathematics > Numerical Analysis

arXiv:2303.05008 (math)
[Submitted on 9 Mar 2023]

Title:Efficient and Parallel Solution of High-order Continuous Time Galerkin for Dissipative and Wave Propagation Problems

Authors:Zhiming Chen, Yong Liu
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Abstract:We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix which allows us to extend the diagonal Padé approximation to solve ordinary differential equations with source terms. The unconditional stability, $hp$ error estimates, and $hp$ superconvergence at the nodes of the continuous time Galerkin method are proved. Numerical examples confirm our theoretical results.
Comments: 34 pages, 1 figure
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M60
Cite as: arXiv:2303.05008 [math.NA]
  (or arXiv:2303.05008v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2303.05008

Submission history

From: Yong Liu [view email]
[v1] Thu, 9 Mar 2023 03:17:47 UTC (2,239 KB)
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