Work

H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions

Year: 2025

Type: article

Abstract: In this work, we show how to impose no-slip boundary conditions for an H ( curl , Ω ) -based formulation for incompressible Stokes flow, which is used in structure-preserving discretizations of Navier-Stokes and magnetohydrodynamics equations. At first glance, it seems straightforward to apply no-slip boundary conditions: the tangential part is an essential boundary condition on H ( curl , Ω ) and the normal component can be naturally enforced through integration-by-parts of the divergence term. However, we show that this can lead to an ill-posed discretization and propose a Nitsche-based finite element method instead. We analyze the discrete system, establishing stability and deriving a priori error estimates. Numerical experiments validate our analysis and demonstrate optimal convergence rates for the velocity field.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2025.118484

Authors: Wietse M. Boon, Wouter Tonnon, Enrico Zampa

Institutions: NORCE Research AS, ETH Zurich, University of Vienna

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,830

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per il Calcolo Scientifico