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25+ years of wavelets for PDEs
Post-edited
Authors : Kunoth, Angela (Author of the conference)
CIRM (Publisher )
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.)
CIRM (Publisher )
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| wavelets in image processing wavelets definition elliptic PDEs beyond finite elements convergence and complexity optimal control Questions of the audience |
Abstract :
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.
MSC Codes : Moreover, wavelet-related concepts have triggered new developments for efficiently solving complex systems of PDEs, as they arise from optimization problems with PDEs.
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.)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 27/09/2016 Conference Date : 20/09/2016 Subseries : Research talks arXiv category : Analysis of PDEs ; Numerical Analysis Mathematical Area(s) : PDE ; Analysis and its Applications ; Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 00:52:07 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-09-20_Kunoth.mp4 
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Information on the Event
Event Title : Multivariate approximation and interpolation with applications - MAIA / Approximation et interpolation à plusieurs variables et applications - MAIAEvent Organizers : Bouhamadi, Abderrahman ; Cohen, Albert ; Conti, Costanza ; Rabut, Christophe Dates : 19/09/2016 - 23/09/2016 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1444.html
Citation Data
DOI : 10.24350/CIRM.V.19051403Cite 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 |
See Also
- [Multi angle] Spherical splines / Author of the conference Prautzsch, Hartmut.
- [Multi angle] Algebraic multigrid and subdivision / Author of the conference Charina, Maria.
- [Multi angle] Some recent insights into computing with positive definite kernels / Author of the conference Fasshauer, Greg.
- [Multi angle] The unitary extension principle on LCA groups / Author of the conference Christensen, Ole.
Bibliography
