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Stokes problem, controlability and radial basis function methods.

Banff International Research Station for Mathematical Innovation and Discovery

Radial basis functions are highly effective meshfree methods for the solution of PDEs problems. In this talk, we first solve a stationary and evolutionary Stokes problem by global and local divergence free RBFs techniques. We prove that, unlike global techniques, local methods are capable of solving large PDEs Stokes problem in an efficient way. We then, use these RBFs methods to solve null control problems for the Stokes system with few internal scalar controls, which are supported in small sets. We recall, that up to the best of our knowledge, Stokes control problems have not been treated in the literature by radial basis functions (RBFs) methods. The RBFs results are compared with classical mixed finite element methods, proving that the proposed meshfree techniques are competitive and more flexible, due to the lack of mesh, than these classical techniques. We close the talk with some open problems and perspectives in this field. Coauthors: Louis David Breton & Cristhian Montoya

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: Universidad Nacional Autónoma de Mexico

2019-03-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68814

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/