2021/05/21 by Haoran Liu, Michael Neilan, Liu, Haoran +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2105.10409
arxiv created 2021/05/21 · openalex publication_date 2021/05/21 · arxiv updated 2021/05/24 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher splits. The velocity space consists of continuous piecewise quadratic polynomials, and the pressure space consists of piecewise linear polynomials without continuity constraints. A Lagrange multiplier space that consists of continuous piecewise quadratic polynomials with respect to boundary partition is introduced to enforce boundary conditions as well as to mitigate the lack of pressure-robustness. We prove several inf-sup conditions, leading to the well-posedness of the method. In addition, we show that the method converges with optimal order and the velocity approximation is divergence free.