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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. 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 ...

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Documents 65N30 | enregistrements trouvés : 133

25+ years of wavelets for PDEs Kunoth, Angela | CIRM H Nouveau

Finite elements in fluids Vol. 4first international symposium on... held at BanffAlbertaCanadaJune 10-13 Gallagher, R. H. ; Norrie, D. H. ; Oden, J. T. ; Zienkiewicz, O. C. | John Wiley And Sons 1982 Nouveau

Finite elemente und differenzenverfahrenspezialtagung uber... 25. bis 27. sept. 1974 in der technischen universitat Clausthal-zellerfeld Albrecht, J. ; Collatz, L. | Birkhäuser Verlag 1975 Nouveau

Topics in numerical analysisproceedings of the s.e.r.c. summer school lancaster#July 19 - Aug. 21 Turner, P. R. | Springer-Verlag 1982 Nouveau

Nonlinear finite element analysis of plates and shellsthe winter annual meeting of the American Society Mechanic EngineeringNov. 15-20 Hughes, Thomas J. R. ; Jay, A. ; Pifko, A. | American Society of Mechanic Engineers 1981 Nouveau

Numerical analysis lancaster 1984 :proceedings of the S.E.R.C. summer school held in lancaster#July 15 - Aug. 3 Turner, P. R. | Springer-Verlag 1985 Nouveau

The mathematical basis of finite element methods with applications to PARTIAL DIFFERENTIAL EQUATIONSbased on lectures at an expository conference on... held at imperial college,u niversity of london,5-7 jan.,1983 Griffiths, D. F. | Clarendon Press 1984 Nouveau

Hybrid and mixed finite element methodspresented at an international symposium to honour professorTheodore H.H. Pian,held at the Georgia Institute of Technology,Atlanta,u.s.a.,8-10 april 1981 Atluri, S. N. ; Gallagher, R. H. ; Zienkiewicz, O. C. | John Wiley And Sons 1983 Nouveau

Optimal controlcalculus of variations, optimal control theory and numerical methodsVariationsrechnung und optimalsteuerungen was held at the mathematisches forschungsinstitut of the University of FreiburgMay 26 - June 1 Bulirsch, R. ; Miele, A. ; Stoer, J. | Birkhäuser Verlag 1993 Nouveau

Preconditioned conjugate gradient methodsproceedings of a conference held in Nijmegen, the Netherlands, June 19-21, 1989 Axelsson, Owe ; Kolotilina, L. Yu. | Springer-Verlag 1990 Nouveau

Numerical analysis of the finite element method Ciarlet, Philippe G. | Les Presse de l'Université de Montréal 1976 Nouveau

Domain decomposition methods in scientific and engineering computing :proceedings of the seventh international conference on domain decomposition methods, which was hosted by the Pennsylvania State University#Oct. 27-30 Keyes, David E. ; Xu, Jinchao | American Mathematical Society 1994 Nouveau

Mathematical aspects of finite element methodsproceedings of the conference held in RomeDec. 10-12 Galligani, I. ; Magenes, E. | Springer-Verlag 1977 Nouveau

Recent advances in numerical methods and applications iiO(h puissance 4) proceedings of the fourth international conference NMA Iliev, O. P. ; Kaschiev, M. S. ; Margenov, S. D. ; Sendov, Bl. H. ; Vassilevski, P. S. | World Scientific 1999 Nouveau

Current trends in scientific computing :ICM 2002 Beijing satellite conference on scientific computing held at Xi'an Jiaotong University#Aug. 15-18 Chen, Zhangxin ; Glowinski, Roland ; Li, Kaitai | American Mathematical Society 2003 Nouveau

Recent advances in adaptative computation :proceedings of the international coference on recent...#May 24-28 Shi, Z. C. ; Chen, Z. ; Tang, T. ; Yu, D. | American Mathematical Society 2005 Nouveau

Multiscale and adaptivity: modeling, numerics and applications.C.I.M.E. summer schoolCetraro # july 6-11, 2009 Naldi, Giovanni ; Russo, Giovanni | Springer;Fondazione CIME 2012 Nouveau

Analytic aspects of problems in Riemannian geometry: elliptic PDEs, solitons and computer imagingLandéda # may 9-13, 2005 Baird, Paul ; El Soufi, A. ; Fardoun, A. ; Regbaoui, R. | Société Mathématique de France 2011 Nouveau

Control and optimization with PDE constraints.Based on the international workshop on control and optimization of PDEsMariatrost # october 10-14, 2011 Bredies, Kristian ; Clason, Christian ; Kunisch, Karl ; von Winckel, Gregory | Birkhäuser 2013 Nouveau

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Finite elements in fluids
Vol. 4
first international symposium on... held at Banff
Alberta
Canada
June 10-13 Gallagher, R. H. ; Norrie, D. H. ; Oden, J. T. ; Zienkiewicz, O. C. | John Wiley And Sons 1982 Nouveau

Finite elemente und differenzenverfahren
spezialtagung uber... 25. bis 27. sept. 1974 in der technischen universitat Clausthal-zellerfeld Albrecht, J. ; Collatz, L. | Birkhäuser Verlag 1975 Nouveau

Topics in numerical analysis
proceedings of the s.e.r.c. summer school lancaster#July 19 - Aug. 21 Turner, P. R. | Springer-Verlag 1982 Nouveau

Nonlinear finite element analysis of plates and shells
the winter annual meeting of the American Society Mechanic Engineering
Nov. 15-20 Hughes, Thomas J. R. ; Jay, A. ; Pifko, A. | American Society of Mechanic Engineers 1981 Nouveau

Numerical analysis lancaster 1984 :
proceedings of the S.E.R.C. summer school held in lancaster#July 15 - Aug. 3 Turner, P. R. | Springer-Verlag 1985 Nouveau

The mathematical basis of finite element methods with applications to PARTIAL DIFFERENTIAL EQUATIONS
based on lectures at an expository conference on... held at imperial college,u niversity of london,5-7 jan.,1983 Griffiths, D. F. | Clarendon Press 1984 Nouveau

Hybrid and mixed finite element methods
presented at an international symposium to honour professorTheodore H.H. Pian,held at the Georgia Institute of Technology,Atlanta,u.s.a.,8-10 april 1981 Atluri, S. N. ; Gallagher, R. H. ; Zienkiewicz, O. C. | John Wiley And Sons 1983 Nouveau

Optimal control
calculus of variations, optimal control theory and numerical methods
Variationsrechnung und optimalsteuerungen was held at the mathematisches forschungsinstitut of the University of Freiburg
May 26 - June 1 Bulirsch, R. ; Miele, A. ; Stoer, J. | Birkhäuser Verlag 1993 Nouveau

Preconditioned conjugate gradient methods
proceedings of a conference held in Nijmegen, the Netherlands, June 19-21, 1989 Axelsson, Owe ; Kolotilina, L. Yu. | Springer-Verlag 1990 Nouveau

Domain decomposition methods in scientific and engineering computing :
proceedings of the seventh international conference on domain decomposition methods, which was hosted by the Pennsylvania State University#Oct. 27-30 Keyes, David E. ; Xu, Jinchao | American Mathematical Society 1994 Nouveau

Mathematical aspects of finite element methods
proceedings of the conference held in Rome
Dec. 10-12 Galligani, I. ; Magenes, E. | Springer-Verlag 1977 Nouveau

Recent advances in numerical methods and applications ii
O(h puissance 4)
proceedings of the fourth international conference NMA Iliev, O. P. ; Kaschiev, M. S. ; Margenov, S. D. ; Sendov, Bl. H. ; Vassilevski, P. S. | World Scientific 1999 Nouveau

Current trends in scientific computing :
ICM 2002 Beijing satellite conference on scientific computing held at Xi'an Jiaotong University#Aug. 15-18 Chen, Zhangxin ; Glowinski, Roland ; Li, Kaitai | American Mathematical Society 2003 Nouveau

Recent advances in adaptative computation :
proceedings of the international coference on recent...#May 24-28 Shi, Z. C. ; Chen, Z. ; Tang, T. ; Yu, D. | American Mathematical Society 2005 Nouveau

Multiscale and adaptivity: modeling, numerics and applications.
C.I.M.E. summer school
Cetraro # july 6-11, 2009 Naldi, Giovanni ; Russo, Giovanni | Springer;Fondazione CIME 2012 Nouveau

Analytic aspects of problems in Riemannian geometry: elliptic PDEs, solitons and computer imaging
Landéda # may 9-13, 2005 Baird, Paul ; El Soufi, A. ; Fardoun, A. ; Regbaoui, R. | Société Mathématique de France 2011 Nouveau

Control and optimization with PDE constraints.
Based on the international workshop on control and optimization of PDEs
Mariatrost # october 10-14, 2011 Bredies, Kristian ; Clason, Christian ; Kunisch, Karl ; von Winckel, Gregory | Birkhäuser 2013 Nouveau