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H 2 25+ years of wavelets for PDEs

Auteurs : Kunoth, Angela (Auteur de la Conférence)
CIRM (Editeur )

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wavelets in image processing wavelets definition elliptic PDEs beyond finite elements convergence and complexity optimal control Questions of the audience

Résumé : Ingrid Daubechies' construction of orthonormal wavelet bases with compact support published in 1988 started a general interest to employ these functions also for the numerical solution of partial differential equations (PDEs). Concentrating on linear elliptic and parabolic PDEs, I will start from theoretical topics such as the well-posedness of the problem in appropriate function spaces and regularity of solutions and will then address quality and optimality of approximations and related concepts from approximation the- ory. We will see that wavelet bases can serve as a basic ingredient, both for the theory as well as for algorithmic realizations. Particularly for situations where solutions exhibit singularities, wavelet concepts enable adaptive appproximations for which convergence and optimal algorithmic complexity can be established. I will describe corresponding implementations based on biorthogonal spline-wavelets.
Moreover, wavelet-related concepts have triggered new developments for efficiently solving complex systems of PDEs, as they arise from optimization problems with PDEs.

Codes MSC :
49J20 - Optimal control problems involving partial differential equations
65N12 - Stability and convergence of numerical methods (BVP of PDE)
65N30 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65T60 - Wavelets (numerical methods)
94A08 - Image processing (compression, reconstruction, etc.)

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 27/09/2016
    Date de captation : 20/09/2016
    Collection : Research talks ; Analysis and its Applications ; Partial Differential Equations
    Format : MP4 (.mp4) - HD
    Durée : 00:52:07
    Domaine : PDE ; Analysis and its Applications ; Numerical Analysis & Scientific Computing
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2016-09-20_Kunoth.mp4

Informations sur la rencontre

Nom de la rencontre : Multivariate approximation and interpolation with applications - MAIA / Approximation et interpolation à plusieurs variables et applications - MAIA
Organisateurs de la rencontre : Bouhamadi, Abderrahman ; Cohen, Albert ; Conti, Costanza ; Rabut, Christophe
Dates : 19/09/2016 - 23/09/2016
Année de la rencontre : 2016
URL Congrès : http://conferences.cirm-math.fr/1444.html

Citation Data

DOI : 10.24350/CIRM.V.19051403
Cite this video as: Kunoth, Angela (2016). 25+ years of wavelets for PDEs. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19051403
URI : http://dx.doi.org/10.24350/CIRM.V.19051403

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