A triangular spectral element method for elliptic and Stokes problems

Jingliang Li, Heping Ma and Huiyuan Li

Applied Mathematics and Computation, 2018, vol. 321, issue C, 195-208

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.

Keywords: Triangule rectangle mapping; Spectral method; General domain; Structured meshes (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:321:y:2018:i:c:p:195-208

DOI: 10.1016/j.amc.2017.10.025

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