Numerical Analysis of Filter Based Stabilization for Evolution Equations
CLEMSON UNIV SC DEPT OF MATHEMATICAL SCIENCES
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We consider filter based stabilization for evolution equations in general and for the Navier-Stokes equations in particular. The first method we consider is to advance in time one time step by a given method and then to apply an uncoupled and modular filter to get the approximation at the new time level. This filter based stabilization, although algorithmically appealing, is viewed in the literature as introducing far too much numerical dissipation to achieve a quality approximate solution. We show that this is indeed the case. We then consider a modification Evolve one time step, Filter, Deconvolve then Relax to get the approximation at the new time step. We give a precise analysis of the numerical diffusion and error in this process and show it has great promise, confirmed in several numerical experiments.
- Numerical Mathematics