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

Mathematics of Computation, vol. 93, pp. 2031–2065

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 R 3 \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

   University of Houston

   Affiliation as printed

   Department of Mathematics, University of Houston, Houston, Texas 77204-3008

2. 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