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A triangular spectral element method for elliptic and Stokes problems

Author

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  • Li, Jingliang
  • Ma, Heping
  • Li, Huiyuan

Abstract

In this paper, we study a triangular spectral-element method based on a one-to-one mapping between the rectangle and the triangle. We construct a new approximation space where the integral singularity brought by the mapping can be removed in a naive and stable way. We build aquasi-interpolation triangular spectral-element approximation, and analyze its approximation error. Based on this quasi-interpolation spectral-element approximation, we put forward a new triangular spectral-element method for the elliptic problems. We present the approximation scheme, analyze the convergence, and do some experiments to test the effectiveness. At last, we implement this triangular spectral-element method to solve the steady Stokes problem.

Suggested Citation

  • Li, Jingliang & Ma, Heping & Li, Huiyuan, 2018. "A triangular spectral element method for elliptic and Stokes problems," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 195-208.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:195-208
    DOI: 10.1016/j.amc.2017.10.025
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