Work

Parametric finite-element discretization of the surface Stokes equations: inf-sup stability and discretization error analysis

Year: 2024

Type: article

Abstract: We study a higher-order surface finite-element penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated, which are equivalent in the continuous setting. The impact of the choice of discretization of the diffusion term and of the divergence term on numerical accuracy and convergence, as well as on implementation advantages, is discussed. We analyse the inf-sup stability of the discrete scheme in a generic approach by lifting stable finite-element pairs known from the literature. A discretization error analysis in tangential norms then shows optimal order convergence of an isogeometric setting that requires only geometric knowledge of the discrete surface.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/drae080

Authors: Hanne Hardering, Simon Praetorius

Institution: Technische Universität Dresden

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G1575401848, G3159387302, G450112389, G7894972749