Finite element error analysis of surface Stokes equations in stream function formulation

ESAIM Mathematical Modelling and Numerical Analysis, vol. 54, pp. 2069–2097

Abstract

We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface Γ ⊂ ℝ3 without boundary. This formulation leads to a coupled system of two second order scalar surface partial differential equations (for the stream function and an auxiliary variable). To this coupled system a trace finite element discretization method is applied. The main topic of the paper is an error analysis of this discretization method, resulting in optimal order discretization error bounds. The analysis applies to the surface finite element method of Dziuk–Elliott, too. We also investigate methods for reconstructing velocity and pressure from the stream function approximation. Results of numerical experiments are included.

Authors 1

1. Arnold Reusken Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany

   Institut für Geometrie und Praktische Mathematik , RWTH-Aachen University , D-52056 , Aachen , Germany