Successive finite element methods for Stokes equations

2021/04/12 by Chunjae Park, Park, Chunjae
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Soil, Finite Element Methods

paper · pdf · doi:10.48550/arxiv.2104.05149

openalex publication_date 2021/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper will suggest a new finite element method to find a P⁴-velocity and a P³-pressure solving Stokes equations. The method solves first the decoupled equation for the P⁴-velocity. Then, four kinds of local P³-pressures and one P⁰-pressure will be calculated in a successive way. If we superpose them, the resulting P³-pressure shows the optimal order of convergence same as a P³-projection. The chief time cost of the new method is on solving two linear systems for the P⁴-velocity and P⁰-pressure, respectively.

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