Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations

Numerical schemes to compute approximate solutions of the evolutionary Stokes and Navier-Stokes equations are studied. The schemes are discontinuous in time and conforming in space and of arbitrarily high order. Fully-discrete error estimates are derived and dependence of the viscosity constant is carefully tracked. It is shown that the errors are bounded by projection errors of the exact solution which exhibit optimal rates when the solutions are smooth.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Konstantinos Chrysafinos, Noel Walkington
• Keywords: Exhibit Optimal Rates, Fully-discrete Error Estimates, MOC 2010, Numerical Schemes, Security Privacy