Numerical solution for an inverse variational problem

Research partially supported by Junta de Andalucía Grant FQM359. Funding for open access charge: Universidad de Granada /CBUA.Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.In the present work, firstly, we use a minimax equality to prove the existence of a solution to a certain system of varitional equations providing a numerical approximation of such a solution. Then, we propose a numerical method to solve a collage-type inverse problem associated with the corresponding system, and illustrate the behaviour of the method with a numerical example.CRUE-CSIC agreementSpringer Natur

Spectral methods for CFD

One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched

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The aim of this work is to analyze some conditions for the existence of solution of a perturbed mixed variational system and that of an associated inverse problem related to the collagebased approach, both on perforated domains or domains with holes. In addition, we study the influence of the size of the holes and state some convergence results. Finally, we conduct a computational study for solving some of those inverse problemsJunta de Andalucía, Project FQM359, and by the “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-MMCIN/AEI/10.13039/501100011033/.Universidad de Granada/CBU

Wavelet and Multiscale Methods

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Stability analysis of the Navier-Stokes velocity tracking problem with bang-bang controls

This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence bang-bang solutions can be expected. We investigate perturbations that account for uncertainty in the tracking data and the initial condition of the state, and analyze the convergence rate of solutions when the original problem is regularized by the Tikhonov term. The stability analysis relies on the H\"older subregularity of the optimality mapping, which stems from the necessary conditions of the problem