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Error Estimates for Finite-Element Navier-Stokes Solvers with Explicit Time Stepping for Pressure
Robert L. Pego
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.
Get the paper in its entierty as06-CNA-005.pdf