An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces

RWTH Publications (RWTH Aachen)

Abstract

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. A complete numerical analysis of the method is presented, including stability, optimal order convergence, and quantification of the geometric errors. Results of numerical experiments are also provided.

Authors 2

1. Maxim A. Olshanskii
2. Arnold Reusken Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen