2020/01/31 by R. W. Thatcher, David J. Silvester, Thatcher, Ronald W. +1
Engineering · #65N15 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2001.11878
openalex publication_date 2020/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By supplementing the pressure space for the Taylor-Hood element a triangular element that satisfies continuity over each element is produced. Making a novel extension of the patch argument to prove stability, this element is shown to be globally stable and give optimal rates of convergence on a wide range of triangular grids. This theoretical result is extended in the discussion given in the appendix, showing how optimal convergence rates can be obtained on all grids. Two examples are presented, one illustrating the convergence rates and the other illustrating difficulties with the Taylor-Hood element which are overcome by the element presented here.