Publication 06-CNA-05

Error Estimates for Finite-Element Navier-Stokes Solvers with Explicit Time Stepping for Pressure

Jian-Guo Liu
Departent of Mathematics &
Institute for Physical Scinece and Technology
University of Maryland
College Park, MD 20742
jliu@math.umd.edu

Jie Liu
Department of Mathematics
University of Maryland
College Park, MD 20742
jieliu@math.umd.edu

and

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon Univeristy
Pittsburgh, PA 15213
rpego@cmu.edu

Abstract: We prove error estimates for a class of finite element schemes for the incompressible Navier-Stokes equations, based upon a recently proved sharp estimate for the commutator of the Laplacian and Helmholtz projection operators. These schemes derive from a fully dissipative unconstrained reformulation of NSE, and were recently proved unconditionally stable by the authors. They require no compatibility condition between finite element spaces for velocity and pressure. Associated numerical computations demonstrate the stability and accuracy of these schemes and of related schemes for which theory is yet lacking.

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