Unconditional Superconvergence Analysis of an Efficient Backward Euler Scheme for Coupled Burgers’ Equations on

Abstract

This paper presents a linearized Backward Euler (BE) scheme for coupled Burgers’ equations. By adopting the temporal-spatial error splitting technique, we rigorously establish the boundedness of numerical solutions in the

H^1

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-norm. By employing the special high-accuracy results of the linear triangular element and the interpolated post-processing approach, we derive unconditional supercloseness and global superconvergence results with order

O(h^2+\tau )

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in

H^1

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-norm on

h^2

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-parallelogram meshes, where h denotes the mesh size and

\tau

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the time step. In addition, the theoretical outcomes and good performance of the proposed scheme are confirmed by numerical experiments.

Keywords

Coupled Burgers’ equations / Temporal-spatial error splitting technique / Unconditional superconvergence result /

h^2

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-parallelogram meshes')">

h^2

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-parallelogram meshes / 65M15 / 65M60 / 65N15 / 65N30

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Funding

National Natural Science Foundation of China(12071443)

the Key Research Project Plan for Higher Education Institutions in Henan Province(25B110023)

the Doctoral Research Foundation of Pingdingshan University(PXY-BSQD-2024003)

RIGHTS & PERMISSIONS

Shanghai University