2021/08/09 by Ioannis P. A. Papadopoulos, Papadopoulos, Ioannis P. A. · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Topology Optimization in Engineering #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2108.03930
arXiv admin note: text overlap with arXiv:2102.10408
openalex publication_date 2021/08/09 · arxiv created 2022/02/20 · arxiv updated 2022/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 H1-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.