Superconvergent and Divergence-Free Finite Element Methods for Stokes Equation

2025/10/16 by Chen, Long, Huang, Xuehai, Zhang, Chao +1
#65N12 #65N22 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2510.14192

Abstract

Superconvergent and divergence-free finite element methods for the Stokes equation are developed. The velocity and pressure are discretized using H(div)-conforming vector elements and discontinuous piecewise polynomials. The discrete formulation employs a weak deviatoric gradient operator built with tangential-normal continuous finite elements for traceless tensors, requiring no stabilization. Optimal and superconvergent error estimates are established. The method connects to nonconforming virtual element and pseudostress-velocity-pressure mixed formulations. Numerical experiments verify the theory.

Citations

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• Divergence-free cut finite element methods for Stokes flow
• A low order divergence-free H(div)-conforming finite element method for Stokes flows
• An unfitted divergence-free higher order finite element method for the Stokes problem