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NUMERICAL ANALYSIS OF A DISCONTINUOUS GALERKIN METHOD FOR THE BORRVALL--PETERSSON TOPOLOGY OPTIMIZATION PROBLEM.
- Source :
- SIAM Journal on Numerical Analysis; 2022, Vol. 60 Issue 5, p2538-2564, 27p
- Publication Year :
- 2022
-
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 [T. Borrvall and J. Petersson, Internat. J. Numer. Methods Fluids, 41 (2003), pp. 77--107]. The convergence results currently found in the literature only consider H¹-conforming discretizations for the velocity. In this work, we extend the numerical analysis of Papadopoulos and S\"uli to divergence-free DG methods with an interior penalty [I. P. A. Papadopoulos and E. S\"uli, J. Comput. Appl. Math., 412 (2022), 114295]. 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 60
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 160061134
- Full Text :
- https://doi.org/10.1137/21M1438943