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Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows

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Abstract

We carry out in this paper a rigorous error analysis for a finite element discretization of the scalar auxiliary variable (SAV) schemes. The finite-element method we study is a Galerkin method with standard Lagrange elements based on a mixed variational formulation. We derive optimal error estimates for both the first- and second-order SAV schemes with the finite-element method in space.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Hongtao Chen, Jingjing Mao & Jie Shen

  2. Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, China

    Hongtao Chen & Jingjing Mao

  3. Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA

    Jie Shen

Authors
  1. Hongtao Chen
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  2. Jingjing Mao
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  3. Jie Shen
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Correspondence to Jie Shen.

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The work of the first and second authors was supported in part by the National Natural Science Foundation of China (No. 11871410), the Natural Science Foundation of Fujian Province of China (No. 2018J01004), the Fundamental Research Funds for the Central Universities (No. 20720180001). The first author also gratefully acknowledges financial support from China Scholarship Council. The work of the third author was supported in part by National Natural Science Foundation of China (No. 11971407).

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Chen, H., Mao, J. & Shen, J. Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Numer. Math. 145, 167–196 (2020). https://doi.org/10.1007/s00211-020-01112-4

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