Efficient, Unconditionally Stable, and Optimally Accurate FE Algorithms for Approximate Deconvolution Models

Abstract

This paper addresses an open question of how to devise numerical schemes for approximate deconvolution fluid flow models that are efficient, unconditionally stable, and optimally accurate. We propose, analyze, and test a scheme for these models that has each of these properties for the case of homogeneous Dirichlet velocity boundary conditions. There are several important components of the derivation, both at the continuous and discrete levels, which allow for these properties to hold. The proofs of stability and convergence are carried out through the use of a special choice of test function and some technical estimates. Numerical tests are provided that confirm the effectiveness of the scheme.