Dahlke, Stephan; Schneider, Cornelia Anisotropic Besov regularity of parabolic PDEs. (English) Zbl 1518.35178 Pure Appl. Funct. Anal. 8, No. 2, 457-476 (2023). MSC: 35B65 35K05 46E35 65M12 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{C. Schneider}, Pure Appl. Funct. Anal. 8, No. 2, 457--476 (2023; Zbl 1518.35178) Full Text: arXiv Link
Dahlke, Stephan; Harbrecht, Helmut; Surowiec, Thomas M. A wavelet-based approach for the simulation and optimal control of nonlocal operator equations. (English) Zbl 1497.49044 SIAM J. Sci. Comput. 44, No. 4, A2691-A2708 (2022). MSC: 49M41 49M15 49M25 65T60 35R11 49J20 65N30 PDFBibTeX XMLCite \textit{S. Dahlke} et al., SIAM J. Sci. Comput. 44, No. 4, A2691--A2708 (2022; Zbl 1497.49044) Full Text: DOI
Dahlke, Stephan; Schneider, Cornelia Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type. (English) Zbl 1478.35063 J. Geom. Anal. 31, No. 12, 11741-11779 (2021). MSC: 35B65 35K35 35K58 46E35 65M12 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{C. Schneider}, J. Geom. Anal. 31, No. 12, 11741--11779 (2021; Zbl 1478.35063) Full Text: DOI arXiv
Dahlke, Stephan; Raasch, Thorsten; Sieber, Alexander Exponential convergence of adaptive quarklet approximation. (English) Zbl 1442.65469 J. Complexity 59, Article ID 101470, 22 p. (2020). MSC: 65T60 42C40 35J15 65N50 PDFBibTeX XMLCite \textit{S. Dahlke} et al., J. Complexity 59, Article ID 101470, 22 p. (2020; Zbl 1442.65469) Full Text: DOI
Dahlke, Stephan; Hansen, Markus; Schneider, Cornelia; Sickel, Winfried On Besov regularity of solutions to nonlinear elliptic partial differential equations. (English) Zbl 1440.35133 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 192, Article ID 111686, 35 p. (2020). Reviewer: Hans Triebel (Jena) MSC: 35J61 35B65 46E35 PDFBibTeX XMLCite \textit{S. Dahlke} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 192, Article ID 111686, 35 p. (2020; Zbl 1440.35133) Full Text: DOI
Dahlke, Stephan (ed.); Kutyniok, Gitta (ed.); Nochetto, Ricardo H. (ed.); Stevenson, Rob (ed.) Innovative approaches to the numerical approximation of PDEs. Abstracts from the workshop held September 1–7, 2019. (English) Zbl 1450.00009 Oberwolfach Rep. 16, No. 3, 2473-2540 (2019). MSC: 00B05 00B25 65-06 65Mxx 35B65 35Q35 35R11 46Exx 65Dxx 65Nxx PDFBibTeX XMLCite \textit{S. Dahlke} (ed.) et al., Oberwolfach Rep. 16, No. 3, 2473--2540 (2019; Zbl 1450.00009) Full Text: DOI
Dahlke, Stephan; Schneider, Cornelia Besov regularity of parabolic and hyperbolic PDEs. (English) Zbl 1420.35055 Anal. Appl., Singap. 17, No. 2, 235-291 (2019). MSC: 35B65 35K55 46E35 65M12 35K20 35L20 35L70 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{C. Schneider}, Anal. Appl., Singap. 17, No. 2, 235--291 (2019; Zbl 1420.35055) Full Text: DOI arXiv
Eckhardt, Frank; Cioica-Licht, Petru A.; Dahlke, Stephan Besov regularity for the stationary Navier-Stokes equation on bounded Lipschitz domains. (English) Zbl 1460.35253 Appl. Anal. 97, No. 3, 466-485 (2018). MSC: 35Q30 35B65 76D05 76D07 42C40 46E35 65T60 PDFBibTeX XMLCite \textit{F. Eckhardt} et al., Appl. Anal. 97, No. 3, 466--485 (2018; Zbl 1460.35253) Full Text: DOI arXiv
Dahlke, Stephan; Schneider, Cornelia Describing the singular behaviour of parabolic equations on cones in fractional Sobolev spaces. (English) Zbl 1415.35145 GEM. Int. J. Geomath. 9, No. 2, 293-315 (2018). MSC: 35K10 35B65 46E35 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{C. Schneider}, GEM. Int. J. Geomath. 9, No. 2, 293--315 (2018; Zbl 1415.35145) Full Text: DOI
Dahlke, Stephan; Diening, Lars; Hartmann, Christoph; Scharf, Benjamin; Weimar, Markus Besov regularity of solutions to the \(p\)-Poisson equation. (English) Zbl 1330.35189 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 130, 298-329 (2016). MSC: 35J92 35B35 41A25 41A46 46E35 65M99 65T60 35B65 35J05 PDFBibTeX XMLCite \textit{S. Dahlke} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 130, 298--329 (2016; Zbl 1330.35189) Full Text: DOI arXiv
Dahlke, Stephan (ed.); Kutyniok, Gitta (ed.); Stevenson, Rob (ed.); Süli, Endre (ed.) New discretization methods for the numerical approximation of PDEs. Abstracts from the workshop held January 11–17, 2015. (English) Zbl 1349.00125 Oberwolfach Rep. 12, No. 1, 87-185 (2015). MSC: 00B05 00B25 65-06 35-06 65Mxx 65Nxx 35A35 35C20 41A25 41A65 42C40 65T60 65F20 PDFBibTeX XMLCite \textit{S. Dahlke} (ed.) et al., Oberwolfach Rep. 12, No. 1, 87--185 (2015; Zbl 1349.00125) Full Text: DOI
Dahlke, Stephan; Weimar, Markus Besov regularity for operator equations on patchwise smooth manifolds. (English) Zbl 1400.46026 Found. Comput. Math. 15, No. 6, 1533-1569 (2015). MSC: 46E35 35B65 42C40 45E99 47B38 65T60 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{M. Weimar}, Found. Comput. Math. 15, No. 6, 1533--1569 (2015; Zbl 1400.46026) Full Text: DOI arXiv
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L. Adaptive wavelet methods for SPDEs. (English) Zbl 1317.60084 Dahlke, Stephan (ed.) et al., Extraction of quantifiable information from complex systems. Cham: Springer (ISBN 978-3-319-08158-8/hbk; 978-3-319-08159-5/ebook). Lecture Notes in Computational Science and Engineering 102, 83-107 (2014). MSC: 60H35 60H15 65C30 65T60 35R60 35B65 60-02 PDFBibTeX XMLCite \textit{P. A. Cioica} et al., Lect. Notes Comput. Sci. Eng. 102, 83--107 (2014; Zbl 1317.60084) Full Text: DOI
Chegini, Nabi G.; Dahlke, Stephan; Friedrich, Ulrich; Stevenson, Rob Piecewise tensor product wavelet bases by extensions and approximation rates. (English) Zbl 1317.65233 Dahlke, Stephan (ed.) et al., Extraction of quantifiable information from complex systems. Cham: Springer (ISBN 978-3-319-08158-8/hbk; 978-3-319-08159-5/ebook). Lecture Notes in Computational Science and Engineering 102, 69-81 (2014). MSC: 65N30 65-02 65T60 65M60 35J60 35K55 65N21 65M32 35R30 PDFBibTeX XMLCite \textit{N. G. Chegini} et al., Lect. Notes Comput. Sci. Eng. 102, 69--81 (2014; Zbl 1317.65233) Full Text: DOI
Ressel, Rudolf; Dülk, Patrick; Dahlke, Stephan; Kazimierski, Kamil S.; Maass, Peter Regularity of the parameter-to-state map of a parabolic partial differential equation. (English) Zbl 1327.35446 Dahlke, Stephan (ed.) et al., Extraction of quantifiable information from complex systems. Cham: Springer (ISBN 978-3-319-08158-8/hbk; 978-3-319-08159-5/ebook). Lecture Notes in Computational Science and Engineering 102, 53-67 (2014). MSC: 35R30 35K20 35Q92 PDFBibTeX XMLCite \textit{R. Ressel} et al., Lect. Notes Comput. Sci. Eng. 102, 53--67 (2014; Zbl 1327.35446) Full Text: DOI
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Friedrich, Ulrich; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L. Convergence analysis of spatially adaptive Rothe methods. (English) Zbl 1309.65107 Found. Comput. Math. 14, No. 5, 863-912 (2014). Reviewer: Fernando Casas (Castellon) MSC: 65M20 65J08 65M22 65T60 35K55 35K90 65M12 PDFBibTeX XMLCite \textit{P. A. Cioica} et al., Found. Comput. Math. 14, No. 5, 863--912 (2014; Zbl 1309.65107) Full Text: DOI
Rashkov, P.; Schmitt, B. A.; Søgaard-Andersen, L.; Lenz, P.; Dahlke, S. A model for ‘antagonistic’ protein dynamics. (English) Zbl 1306.92019 Int. J. Biomath. Biostat. 2, No. 1, 75-85 (2013). MSC: 92C40 35K57 35B35 PDFBibTeX XMLCite \textit{P. Rashkov} et al., Int. J. Biomath. Biostat. 2, No. 1, 75--85 (2013; Zbl 1306.92019)
Chegini, Nabi; Dahlke, Stephan; Friedrich, Ulrich; Stevenson, Rob Piecewise tensor product wavelet bases by extensions and approximation rates. (English) Zbl 1277.65093 Math. Comput. 82, No. 284, 2157-2190 (2013). Reviewer: Manfred Tasche (Rostock) MSC: 65N30 65T60 65N12 46E35 35B65 41A25 35J05 65N55 PDFBibTeX XMLCite \textit{N. Chegini} et al., Math. Comput. 82, No. 284, 2157--2190 (2013; Zbl 1277.65093) Full Text: DOI
Rashkov, Peter; Schmitt, Bernhard A.; Søgaard-Andersen, Lotte; Lenz, Peter; Dahlke, Stephan A model of oscillatory protein dynamics in bacteria. (English) Zbl 1254.92029 Bull. Math. Biol. 74, No. 9, 2183-2203 (2012). MSC: 92C40 92C05 35K57 35Q92 37N25 PDFBibTeX XMLCite \textit{P. Rashkov} et al., Bull. Math. Biol. 74, No. 9, 2183--2203 (2012; Zbl 1254.92029) Full Text: DOI
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L. Adaptive wavelet methods for the stochastic Poisson equation. (English) Zbl 1260.65003 BIT 52, No. 3, 589-614 (2012). Reviewer: Dominique Lepingle (Orléans) MSC: 65C30 60H15 60H35 35R60 65T60 PDFBibTeX XMLCite \textit{P. A. Cioica} et al., BIT 52, No. 3, 589--614 (2012; Zbl 1260.65003) Full Text: DOI
Bonesky, Thomas; Dahlke, Stephan; Maass, Peter; Raasch, Thorsten Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems. (English) Zbl 1207.65114 Adv. Comput. Math. 33, No. 4, 385-411 (2010). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M32 35K05 35R30 65M60 65T60 80A23 80M25 PDFBibTeX XMLCite \textit{T. Bonesky} et al., Adv. Comput. Math. 33, No. 4, 385--411 (2010; Zbl 1207.65114) Full Text: DOI
Dahlke, Stephan; Sickel, Winfried Besov regularity for the Poisson equation in smooth and polyhedral cones. (English) Zbl 1169.35018 Maz’ya, Vladimir (ed.), Sobolev spaces in mathematics II. Applications in analysis and partial differential equations. New York, NY: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher (ISBN 978-0-387-85649-0/hbk; 978-0-387-85650-6/e-book; 978-0-387-85791-6/set). International Mathematical Series 9, 123-145 (2009). Reviewer: Dian K. Palagachev (Bari) MSC: 35J25 65T60 35B65 35D10 35J05 46E35 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{W. Sickel}, in: Sobolev spaces in mathematics II. Applications in analysis and partial differential equations. New York, NY: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher. 123--145 (2009; Zbl 1169.35018) Full Text: DOI
Dahlke, Stephan; Raasch, Thorsten; Werner, Manuel; Fornasier, Massimo; Stevenson, Rob Adaptive frame methods for elliptic operator equations: The steepest descent approach. (English) Zbl 1153.65050 IMA J. Numer. Anal. 27, No. 4, 717-740 (2007). Reviewer: Werner H. Schmidt (Greifswald) MSC: 65J10 35P99 PDFBibTeX XMLCite \textit{S. Dahlke} et al., IMA J. Numer. Anal. 27, No. 4, 717--740 (2007; Zbl 1153.65050) Full Text: DOI
Dahlke, Stephan; Fornasier, Massimo; Raasch, Thorsten Adaptive frame methods for elliptic operator equations. (English) Zbl 1122.65103 Adv. Comput. Math. 27, No. 1, 27-63 (2007). Reviewer: Dietrich Braess (Bochum) MSC: 65N22 65N55 65F10 65F50 65N12 65T60 35J55 PDFBibTeX XMLCite \textit{S. Dahlke} et al., Adv. Comput. Math. 27, No. 1, 27--63 (2007; Zbl 1122.65103) Full Text: DOI
Dahlke, Stephan; Novak, Erich; Sickel, Winfried Optimal approximation of elliptic problems by linear and nonlinear mappings. II. (English) Zbl 1102.65061 J. Complexity 22, No. 4, 549-603 (2006). MSC: 65J10 47A50 35J05 65N30 65N15 65Y20 PDFBibTeX XMLCite \textit{S. Dahlke} et al., J. Complexity 22, No. 4, 549--603 (2006; Zbl 1102.65061) Full Text: DOI arXiv
Barinka, Arne; Dahlke, Stephan; Dahmen, Wolfgang Adaptive application of operators in standard representation. (English) Zbl 1101.65111 Adv. Comput. Math. 24, No. 1-4, 5-34 (2006). Reviewer: Iulian Coroian (Baia Mare) MSC: 65N38 65J10 65N12 65N55 65T60 35J25 47A50 PDFBibTeX XMLCite \textit{A. Barinka} et al., Adv. Comput. Math. 24, No. 1--4, 5--34 (2006; Zbl 1101.65111) Full Text: DOI
Dahlke, Stephan; Novak, Erich; Sickel, Winfried Optimal approximation of elliptic problems by linear and nonlinear mappings. I. (English) Zbl 1092.65044 J. Complexity 22, No. 1, 29-49 (2006). MSC: 65J10 47A50 42C40 35J05 65N30 65T60 65N15 PDFBibTeX XMLCite \textit{S. Dahlke} et al., J. Complexity 22, No. 1, 29--49 (2006; Zbl 1092.65044) Full Text: DOI arXiv
Dahlke, Stephan; Fornasier, Massimo; Raasch, Thorsten Adaptive frame algorithms for elliptic operator equations. (English) Zbl 1391.65174 PAMM, Proc. Appl. Math. Mech. 5, 763-764 (2005). MSC: 65N22 65N55 65F10 65F50 65N12 65T60 35J56 PDFBibTeX XMLCite \textit{S. Dahlke} et al., PAMM, Proc. Appl. Math. Mech. 5, 763--764 (2005; Zbl 1391.65174) Full Text: DOI
Böhmer, Klaus; Dahlke, Stephan Stability and convergence for discretization methods with applications to wavelet Galerkin schemes. (English) Zbl 1050.65096 Int. J. Pure Appl. Math. 6, No. 4, 465-489 (2003). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65N12 65N30 35J65 35B32 65T60 PDFBibTeX XMLCite \textit{K. Böhmer} and \textit{S. Dahlke}, Int. J. Pure Appl. Math. 6, No. 4, 465--489 (2003; Zbl 1050.65096)
Dahlke, Stephan; Maaß, Peter An outline of adaptive wavelet Galerkin methods for Tikhonov regularization of inverse parabolic problems. (English) Zbl 1037.65055 Hon, Yiu-Chung (ed.) et al., Recent development in theories and numerics. Proceedings of the international conference on inverse problems, Hong Kong, China, January 9–12, 2002. River Edge, NJ: World Scientific (ISBN 981-238-366-2/pbk). 56-66 (2003). MSC: 65J10 65M32 65R30 35K05 65J22 47A52 65M20 65T60 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{P. Maaß}, in: Recent development in theories and numerics. Proceedings of the international conference on inverse problems, Hong Kong, China, January 9--12, 2002. River Edge, NJ: World Scientific. 56--66 (2003; Zbl 1037.65055)
Dahlke, Stephan Besov regularity for the Neumann problem. (English) Zbl 1109.35023 Haroske, Dorothee (ed.) et al., Function spaces, differential operators and nonlinear analysis. The Hans Triebel anniversary volume. Based on the lectures given at the international conference on function spaces, differential operators and nonlinear analysis, FSDONA-01, Teistungen, Germany, June 28–July 4, 2001, in honor of the 65th birthday of H. J. Triebel. Basel: Birkhäuser (ISBN 3-7643-6935-3/hbk). 267-277 (2003). Reviewer: Lubomira Softova (Bari) MSC: 35B65 35J65 46E35 PDFBibTeX XMLCite \textit{S. Dahlke}, in: Function spaces, differential operators and nonlinear analysis. The Hans Triebel anniversary volume. Based on the lectures given at the international conference on function spaces, differential operators and nonlinear analysis, FSDONA-01, Teistungen, Germany, June 28--July 4, 2001, in honor of the 65th birthday of H. J. Triebel. Basel: Birkhäuser. 267--277 (2003; Zbl 1109.35023)
Dahlke, Stephan Besov regularity of edge singularities for the Poisson equation in polyhedral domains. (English) Zbl 1071.65172 Numer. Linear Algebra Appl. 9, No. 6-7, 457-466 (2002). MSC: 65N99 35B65 PDFBibTeX XMLCite \textit{S. Dahlke}, Numer. Linear Algebra Appl. 9, No. 6--7, 457--466 (2002; Zbl 1071.65172) Full Text: DOI
Dahlke, Stephan; Dahmen, Wolfgang; Urban, Karsten Adaptive wavelet methods for saddle point problems – optimal convergence rates. (English) Zbl 1024.65101 SIAM J. Numer. Anal. 40, No. 4, 1230-1262 (2002). MSC: 65N12 65T60 41A46 42C40 46E35 65N22 65N55 35B65 PDFBibTeX XMLCite \textit{S. Dahlke} et al., SIAM J. Numer. Anal. 40, No. 4, 1230--1262 (2002; Zbl 1024.65101) Full Text: DOI
Barinka, Arne; Barsch, Titus; Charton, Philippe; Cohen, Albert; Dahlke, Stephan; Dahmen, Wolfgang; Urban, Karsten Adaptive wavelet schemes for elliptic problems–implementation and numerical experiments. (English) Zbl 1016.65090 SIAM J. Sci. Comput. 23, No. 3, 910-939 (2001). MSC: 65N30 65N12 65N15 65T60 35J25 65N55 65F30 PDFBibTeX XMLCite \textit{A. Barinka} et al., SIAM J. Sci. Comput. 23, No. 3, 910--939 (2001; Zbl 1016.65090) Full Text: DOI
Dahlke, Stephan Besov regularity for the Stokes problem. (English) Zbl 0947.35107 Haußmann, Werner (ed.) et al., Advances in multivariate approximation. Proceedings of the 3rd international conference on multivariate approximation theory, Witten-Bommerholz, Germany, September 27-October 2, 1998. Berlin: Wiley-VCH. Math. Res. 107, 129-138 (1999). MSC: 35Q30 76D03 PDFBibTeX XMLCite \textit{S. Dahlke}, Math. Res. 107, 129--138 (1999; Zbl 0947.35107)
Dahlke, S. Besov regularity for elliptic boundary value problems in polygonal domains. (English) Zbl 0940.35064 Appl. Math. Lett. 12, No. 6, 31-36 (1999). MSC: 35J15 42C40 35B65 PDFBibTeX XMLCite \textit{S. Dahlke}, Appl. Math. Lett. 12, No. 6, 31--36 (1999; Zbl 0940.35064) Full Text: DOI
Dahlke, S. Besov regularity for interface problems. (English) Zbl 0928.35025 ZAMM, Z. Angew. Math. Mech. 79, No. 6, 383-388 (1999). MSC: 35B65 41A46 46E35 PDFBibTeX XMLCite \textit{S. Dahlke}, ZAMM, Z. Angew. Math. Mech. 79, No. 6, 383--388 (1999; Zbl 0928.35025) Full Text: DOI
Dahlke, Stephan Besov regularity for second order elliptic boundary value problems with variable coefficients. (English) Zbl 0895.35017 Manuscr. Math. 95, No. 1, 59-77 (1998). MSC: 35B65 41A46 31B10 65N30 35J25 PDFBibTeX XMLCite \textit{S. Dahlke}, Manuscr. Math. 95, No. 1, 59--77 (1998; Zbl 0895.35017) Full Text: DOI EuDML
Dahlke, Stephan; Dahmen, Wolfgang; Hochmuth, Reinhard; Schneider, Reinhold Stable multiscale bases and local error estimation for elliptic problems. (English) Zbl 0872.65098 Appl. Numer. Math. 23, No. 1, 21-47 (1997). Reviewer: S.Migorski (Krakow) MSC: 65N15 65N12 65N30 35J25 PDFBibTeX XMLCite \textit{S. Dahlke} et al., Appl. Numer. Math. 23, No. 1, 21--47 (1997; Zbl 0872.65098) Full Text: DOI
Dahlke, Stephan; DeVore, Ronald A. Besov regularity for elliptic boundary value problems. (English) Zbl 0883.35018 Commun. Partial Differ. Equations 22, No. 1-2, 1-16 (1997). Reviewer: E.Minchev (Sofia) MSC: 35B65 35J25 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{R. A. DeVore}, Commun. Partial Differ. Equations 22, No. 1--2, 1--16 (1997; Zbl 0883.35018) Full Text: DOI
Dahlke, Stephan; Weinreich, Ilona Wavelet bases adapted to pseudodifferential operators. (English) Zbl 0806.65112 Appl. Comput. Harmon. Anal. 1, No. 3, 267-283 (1994). Reviewer: J.Elschner (Berlin) MSC: 65N30 35S15 PDFBibTeX XMLCite \textit{S. Dahlke} and \textit{I. Weinreich}, Appl. Comput. Harmon. Anal. 1, No. 3, 267--283 (1994; Zbl 0806.65112) Full Text: DOI Link