Pressure-Robust Fortin-Soulie Elements of the Stokes Equation on Curved Domains
It provides a pressure-robust method for Stokes equations on curved domains, which is an incremental improvement over existing methods for flat domains.
This paper develops a pressure-robust, divergence-free nonconforming finite element method for the Stokes problem on curved domains, achieving optimal convergence rates. Numerical examples validate the theoretical results.
This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the Fortin-Soulie element from a reference triangle using an isoparametric mapping for the geometry and a Piola transform for the function space. The inf-sup condition and the error estimate with optimal convergence rate are proved. Pressure-robustness is obtained by replacing the discrete velocity test functions with the first-order Raviart-Thomas functions. Numerical examples are provided to validate the theoretical results.