Numerical analysis of a discontinuous Galerkin method for the Borrvall-Petersson topology optimization problem
Abstract
Divergence-free discontinuous Galerkin (DG) finite element methods offer a suitable discretization for the pointwise divergence-free numerical solution of Borrvall and Petersson's model for the topology optimization of fluids in Stokes flow [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107]. The convergence results currently found in literature only consider H^1-conforming discretizations for the velocity. In this work, we extend the numerical analysis of Papadopoulos and Suli to divergence-free DG methods with an interior penalty [I. P. A. Papadopoulos and E. Suli, Numerical analysis of a topology optimization problem for Stokes flow, arXiv preprint arXiv:2102.10408, (2021)]. We show that, given an isolated minimizer of the infinite-dimensional problem, there exists a sequence of DG finite element solutions, satisfying necessary first-order optimality conditions, that strongly converges to the minimizer.
Keywords
Cite
@article{arxiv.2108.03930,
title = {Numerical analysis of a discontinuous Galerkin method for the Borrvall-Petersson topology optimization problem},
author = {Ioannis P. A. Papadopoulos},
journal= {arXiv preprint arXiv:2108.03930},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2102.10408