Numerical analysis of a discontinuous Galerkin method for the Borrvall-Petersson topology optimization problem
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, Inter...
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Format | Journal Article |
Language | English |
Published |
09.08.2021
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Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2108.03930 |