Convergence rate of the spectral difference method on regular triangular
 meshes

Pavel Alexeevisch Bakhvalov

doi:10.48550/arxiv.2404.10391

April 16, 2024Open Access

Convergence rate of the spectral difference method on regular triangular meshes

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Key Points

Convergence rates depend directly on whether transport velocity aligns with mesh edges in the spectral difference method scheme.
Order p convergence occurs when velocity is parallel to mesh edges, whereas nonparallel flow achieves an improved order of p+1.
Theoretical analysis verifies the convergence behavior for p=1, while numerical experiments confirm orders p=1, 2, and 3 across meshes.

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Implication

Theoretical analysis demonstrates variable convergence orders for scalar transport equations on regular triangular meshes, highlighting edge alignment effects.

Abstract

We consider the spectral difference method based on the p-th order Raviart~-- Thomas space (p=1,2,3) on regular triangular meshes for the scalar transport equation. The solution converges with the order p if the transport velocity is parallel to a family of mesh edges and with the order p+1 otherwise. We prove this fact for p=1 and show it for p=1,2,3 in numerical experiments.

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Pavel Alexeevisch Bakhvalov (2024) studied this question.

synapsesocial.com/papers/68e6ef30b6db64358766a6fc https://doi.org/10.48550/arxiv.2404.10391

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Convergence rate of the spectral difference method on regular triangular meshes

Key Points

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Implication

Abstract

Discussion

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Convergence rate of the spectral difference method on regular triangular meshes

Key Points

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Implication

Abstract

Discussion

Cite This Study

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