Qiqi Rao, Doctor, The Hong Kong Polytechnic University

Wei Gong, Associate Professor

Optimal Convergence of Arbitrary Lagrangian-Eulerian Finite Element Methods for the Stokes Equation in an Evolving Domain

9:00-10:00 July 18(Thursday), Z301

The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method along the trajectories of the evolving mesh. The error of the semidiscrete arbitrary Lagrangian- Eulerian method is shown to be O(h^(r+1)) for velocity in L∞(0,T;L^2) norm and O(h^r) for pressure in L2(0,T;L^2) norm by employing the Taylor–Hood finite elements of degree r ≥ 2, using Nitsche’s duality argument adapted to an evolving mesh, by proving that the material derivative and the Stokes–Ritz projection commute up to terms which have optimal-order convergence in the L^2 norm. Numerical examples are provided to support the theoretical analysis.