Banjai, Lehel; Melenk, Jens M.; Schwab, Christoph \(hp\)-FEM for reaction-diffusion equations. II: Robust exponential convergence for multiple length scales in corner domains. (English) Zbl 07800835 IMA J. Numer. Anal. 43, No. 6, 3282-3325 (2023). MSC: 65N30 65N35 65N12 35B25 35B65 26A33 35R11 PDFBibTeX XMLCite \textit{L. Banjai} et al., IMA J. Numer. Anal. 43, No. 6, 3282--3325 (2023; Zbl 07800835) Full Text: DOI arXiv
Faustmann, Markus; Marcati, Carlo; Melenk, Jens Markus; Schwab, Christoph Exponential convergence of \(hp\)-FEM for the integral fractional Laplacian in polygons. (English) Zbl 07770179 SIAM J. Numer. Anal. 61, No. 6, 2601-2622 (2023). MSC: 65N30 65N12 65N15 26A33 35R11 PDFBibTeX XMLCite \textit{M. Faustmann} et al., SIAM J. Numer. Anal. 61, No. 6, 2601--2622 (2023; Zbl 07770179) Full Text: DOI arXiv
Aylwin, Rubén; Henríquez, Fernando; Schwab, Christoph ReLU neural network Galerkin BEM. (English) Zbl 07698915 J. Sci. Comput. 95, No. 2, Paper No. 41, 37 p. (2023). MSC: 65Nxx 35Jxx 68Txx PDFBibTeX XMLCite \textit{R. Aylwin} et al., J. Sci. Comput. 95, No. 2, Paper No. 41, 37 p. (2023; Zbl 07698915) Full Text: DOI
Gonon, Lukas; Schwab, Christoph Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations. (English) Zbl 07652560 Anal. Appl., Singap. 21, No. 1, 1-47 (2023). MSC: 68T07 45K05 60H35 PDFBibTeX XMLCite \textit{L. Gonon} and \textit{C. Schwab}, Anal. Appl., Singap. 21, No. 1, 1--47 (2023; Zbl 07652560) Full Text: DOI arXiv
Banjai, Lehel; Melenk, Jens M.; Schwab, Christoph Exponential convergence of hp FEM for spectral fractional diffusion in polygons. (English) Zbl 1511.65117 Numer. Math. 153, No. 1, 1-47 (2023). MSC: 65N30 65N50 65N12 65N15 35J86 35B35 26A33 35R11 PDFBibTeX XMLCite \textit{L. Banjai} et al., Numer. Math. 153, No. 1, 1--47 (2023; Zbl 1511.65117) Full Text: DOI arXiv
Faustmann, Markus; Marcati, Carlo; Melenk, Jens Markus; Schwab, Christoph Weighted analytic regularity for the integral fractional Laplacian in polyhedra. arXiv:2307.11679 Preprint, arXiv:2307.11679 [math.AP] (2023). MSC: 26A33 35A20 35B45 35J70 35R11 BibTeX Cite \textit{M. Faustmann} et al., ``Weighted analytic regularity for the integral fractional Laplacian in polyhedra'', Preprint, arXiv:2307.11679 [math.AP] (2023) Full Text: arXiv OA License
Faustmann, Markus; Marcati, Carlo; Melenk, Jens Markus; Schwab, Christoph Weighted analytic regularity for the integral fractional Laplacian in polygons. (English) Zbl 1505.35070 SIAM J. Math. Anal. 54, No. 6, 6323-6357 (2022). MSC: 35B65 26A33 35A20 35B45 35J25 35J70 35R11 PDFBibTeX XMLCite \textit{M. Faustmann} et al., SIAM J. Math. Anal. 54, No. 6, 6323--6357 (2022; Zbl 1505.35070) Full Text: DOI arXiv
Bansal, Pratyuksh; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph Space-time discontinuous Galerkin approximation of acoustic waves with point singularities. (English) Zbl 07528299 IMA J. Numer. Anal. 41, No. 3, 2056-2109 (2021). MSC: 65Mxx PDFBibTeX XMLCite \textit{P. Bansal} et al., IMA J. Numer. Anal. 41, No. 3, 2056--2109 (2021; Zbl 07528299) Full Text: DOI arXiv
Longo, Marcello; Mishra, Siddhartha; Rusch, T. Konstantin; Schwab, Christoph Higher-order quasi-Monte Carlo training of deep neural networks. (English) Zbl 1492.65043 SIAM J. Sci. Comput. 43, No. 6, A3938-A3966 (2021). MSC: 65D15 65C05 68T07 65D30 35R60 PDFBibTeX XMLCite \textit{M. Longo} et al., SIAM J. Sci. Comput. 43, No. 6, A3938--A3966 (2021; Zbl 1492.65043) Full Text: DOI arXiv
Gonon, Lukas; Schwab, Christoph Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models. (English) Zbl 1475.91356 Finance Stoch. 25, No. 4, 615-657 (2021). Reviewer: George Stoica (Saint John) MSC: 91G20 68T07 60G51 45K05 91G80 PDFBibTeX XMLCite \textit{L. Gonon} and \textit{C. Schwab}, Finance Stoch. 25, No. 4, 615--657 (2021; Zbl 1475.91356) Full Text: DOI arXiv
Hoang, Viet Ha; Quek, Jia Hao; Schwab, Christoph Multilevel Markov chain Monte Carlo for Bayesian inversion of parabolic partial differential equations under Gaussian prior. (English) Zbl 1465.65006 SIAM/ASA J. Uncertain. Quantif. 9, 384-419 (2021). MSC: 65C30 65C05 35R30 35R60 60G60 60H15 60H35 PDFBibTeX XMLCite \textit{V. H. Hoang} et al., SIAM/ASA J. Uncertain. Quantif. 9, 384--419 (2021; Zbl 1465.65006) Full Text: DOI
Herrmann, Lukas; Keller, Magdalena; Schwab, Christoph Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. (English) Zbl 1478.65107 Math. Comput. 90, No. 330, 1831-1860 (2021). MSC: 65N21 62F15 65C05 65N30 35R30 35R60 PDFBibTeX XMLCite \textit{L. Herrmann} et al., Math. Comput. 90, No. 330, 1831--1860 (2021; Zbl 1478.65107) Full Text: DOI
Hoang, Viet Ha; Quek, Jia Hao; Schwab, Christoph Analysis of a multilevel Markov chain Monte Carlo finite element method for Bayesian inversion of log-normal diffusions. (English) Zbl 1491.65010 Inverse Probl. 36, No. 3, Article ID 035021, 46 p. (2020). MSC: 65C05 65N30 65N21 35R30 62F15 60H15 65N12 PDFBibTeX XMLCite \textit{V. H. Hoang} et al., Inverse Probl. 36, No. 3, Article ID 035021, 46 p. (2020; Zbl 1491.65010) Full Text: DOI
Herrmann, Lukas; Kirchner, Kristin; Schwab, Christoph Multilevel approximation of Gaussian random fields: fast simulation. (English) Zbl 1448.60110 Math. Models Methods Appl. Sci. 30, No. 1, 181-223 (2020). MSC: 60G60 35R11 35R60 65C40 65N30 PDFBibTeX XMLCite \textit{L. Herrmann} et al., Math. Models Methods Appl. Sci. 30, No. 1, 181--223 (2020; Zbl 1448.60110) Full Text: DOI
Zech, Jakob; Dũng, Dinh; Schwab, Christoph Multilevel approximation of parametric and stochastic PDES. (English) Zbl 1427.65386 Math. Models Methods Appl. Sci. 29, No. 9, 1753-1817 (2019). MSC: 65N30 35A20 35B30 32D05 65D30 35R60 65N15 65N12 65F15 PDFBibTeX XMLCite \textit{J. Zech} et al., Math. Models Methods Appl. Sci. 29, No. 9, 1753--1817 (2019; Zbl 1427.65386) Full Text: DOI
Herrmann, Lukas; Schwab, Christoph Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients. (English) Zbl 07135561 ESAIM, Math. Model. Numer. Anal. 53, No. 5, 1507-1552 (2019). MSC: 65D30 65N30 60G60 PDFBibTeX XMLCite \textit{L. Herrmann} and \textit{C. Schwab}, ESAIM, Math. Model. Numer. Anal. 53, No. 5, 1507--1552 (2019; Zbl 07135561) Full Text: DOI Link
Herrmann, Lukas; Schwab, Christoph; Zech, Jakob Uncertainty quantification for spectral fractional diffusion: sparsity analysis of parametric solutions. (English) Zbl 1469.65170 SIAM/ASA J. Uncertain. Quantif. 7, 913-947 (2019). Reviewer: Muhammad Hassan (Aachen) MSC: 65N75 65C05 26A33 35R11 65N12 PDFBibTeX XMLCite \textit{L. Herrmann} et al., SIAM/ASA J. Uncertain. Quantif. 7, 913--947 (2019; Zbl 1469.65170) Full Text: DOI
Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph Tensor FEM for spectral fractional diffusion. (English) Zbl 1429.65272 Found. Comput. Math. 19, No. 4, 901-962 (2019). MSC: 65N30 35J25 35R11 65N12 PDFBibTeX XMLCite \textit{L. Banjai} et al., Found. Comput. Math. 19, No. 4, 901--962 (2019; Zbl 1429.65272) Full Text: DOI arXiv
Herrmann, Lukas; Schwab, Christoph QMC algorithms with product weights for lognormal-parametric, elliptic PDEs. (English) Zbl 1422.65017 Owen, Art B. (ed.) et al., Monte Carlo and quasi-Monte Carlo methods, MCQMC 2016. Proceedings of the 12th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Stanford, CA, August 14–19, 2016. Cham: Springer. Springer Proc. Math. Stat. 241, 313-330 (2018). Reviewer: Eric Chung (Hong Kong) MSC: 65C05 65D30 35J15 35R60 65N15 65N75 PDFBibTeX XMLCite \textit{L. Herrmann} and \textit{C. Schwab}, Springer Proc. Math. Stat. 241, 313--330 (2018; Zbl 1422.65017) Full Text: DOI
Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. Large deformation shape uncertainty quantification in acoustic scattering. (English) Zbl 1402.35321 Adv. Comput. Math. 44, No. 5, 1475-1518 (2018). MSC: 35R60 60H35 65N75 65N12 76Q05 76M28 PDFBibTeX XMLCite \textit{R. Hiptmair} et al., Adv. Comput. Math. 44, No. 5, 1475--1518 (2018; Zbl 1402.35321) Full Text: DOI
Herrmann, Lukas; Lang, Annika; Schwab, Christoph Numerical analysis of lognormal diffusions on the sphere. (English) Zbl 1402.60062 Stoch. Partial Differ. Equ., Anal. Comput. 6, No. 1, 1-44 (2018). MSC: 60G60 60G15 60H15 60H35 65C30 PDFBibTeX XMLCite \textit{L. Herrmann} et al., Stoch. Partial Differ. Equ., Anal. Comput. 6, No. 1, 1--44 (2018; Zbl 1402.60062) Full Text: DOI arXiv
Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska Correction to: “Multilevel Monte Carlo front-tracking for random scalar conservation laws”. (English) Zbl 1430.65004 BIT 58, No. 1, 247-255 (2018). MSC: 65C30 35L65 65C05 65M06 65M12 60H15 60H35 35R60 65Y20 65M75 PDFBibTeX XMLCite \textit{N. H. Risebro} et al., BIT 58, No. 1, 247--255 (2018; Zbl 1430.65004) Full Text: DOI
Gantner, Robert N.; Herrmann, Lukas; Schwab, Christoph Quasi-Monte Carlo integration for affine-parametric, elliptic PDEs: local supports and product weights. (English) Zbl 1378.65072 SIAM J. Numer. Anal. 56, No. 1, 111-135 (2018). MSC: 65D30 65N30 65C05 PDFBibTeX XMLCite \textit{R. N. Gantner} et al., SIAM J. Numer. Anal. 56, No. 1, 111--135 (2018; Zbl 1378.65072) Full Text: DOI
Mishra, Siddhartha; Schwab, Christoph Monte-Carlo finite-volume methods in uncertainty quantification for hyperbolic conservation laws. (English) Zbl 1407.65150 Jin, Shi (ed.) et al., Uncertainty quantification for hyperbolic and kinetic equations. Cham: Springer. SEMA SIMAI Springer Ser. 14, 231-277 (2017). Reviewer: Hang Lau (Montréal) MSC: 65M08 65C05 35L65 PDFBibTeX XMLCite \textit{S. Mishra} and \textit{C. Schwab}, SEMA SIMAI Springer Ser. 14, 231--277 (2017; Zbl 1407.65150) Full Text: DOI
Bachmayr, Markus; Cohen, Albert; Dũng, Dinh; Schwab, Christoph Fully discrete approximation of parametric and stochastic elliptic PDEs. (English) Zbl 1377.65005 SIAM J. Numer. Anal. 55, No. 5, 2151-2186 (2017). MSC: 65C30 60H15 35R60 60H35 65N30 65T60 65N12 PDFBibTeX XMLCite \textit{M. Bachmayr} et al., SIAM J. Numer. Anal. 55, No. 5, 2151--2186 (2017; Zbl 1377.65005) Full Text: DOI arXiv
Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. (English) Zbl 1347.65012 SIAM J. Numer. Anal. 54, No. 4, 2541-2568 (2016). MSC: 65C30 60H15 35J47 35R60 65C05 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{J. Dick} et al., SIAM J. Numer. Anal. 54, No. 4, 2541--2568 (2016; Zbl 1347.65012) Full Text: DOI arXiv
Mishra, Siddhartha; Risebro, Nils Henrik; Schwab, Christoph; Tokareva, Svetlana Numerical solution of scalar conservation laws with random flux functions. (English) Zbl 1343.65007 SIAM/ASA J. Uncertain. Quantif. 4, 552-591 (2016). MSC: 65C30 60H15 60H35 35R60 65C05 65M08 35L65 PDFBibTeX XMLCite \textit{S. Mishra} et al., SIAM/ASA J. Uncertain. Quantif. 4, 552--591 (2016; Zbl 1343.65007) Full Text: DOI Link
Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska Multilevel Monte Carlo front-tracking for random scalar conservation laws. (English) Zbl 1350.65008 BIT 56, No. 1, 263-292 (2016); correction ibid. 58, No. 1, 247-255 (2018). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C30 35L65 65C05 65M06 65M12 60H15 60H35 35R60 65Y20 65M75 PDFBibTeX XMLCite \textit{N. H. Risebro} et al., BIT 56, No. 1, 263--292 (2016; Zbl 1350.65008) Full Text: DOI Link
Lang, Annika; Schwab, Christoph Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations. (English) Zbl 1328.60126 Ann. Appl. Probab. 25, No. 6, 3047-3094 (2015). MSC: 60G60 60G15 60G17 60H15 60H35 33C55 41A25 65C30 65T50 65N30 PDFBibTeX XMLCite \textit{A. Lang} and \textit{C. Schwab}, Ann. Appl. Probab. 25, No. 6, 3047--3094 (2015; Zbl 1328.60126) Full Text: DOI arXiv Euclid
Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes. (English) Zbl 1335.65006 ESAIM, Math. Model. Numer. Anal. 49, No. 5, 1367-1398 (2015). Reviewer: Dominique Lepingle (Orléans) MSC: 65C30 65N30 35R60 60H35 65N12 65N22 60H15 65N15 PDFBibTeX XMLCite \textit{M. Eigel} et al., ESAIM, Math. Model. Numer. Anal. 49, No. 5, 1367--1398 (2015; Zbl 1335.65006) Full Text: DOI Link
Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H. Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. (English) Zbl 1341.65003 Numer. Math. 131, No. 2, 329-368 (2015). Reviewer: Jaromir Antoch (Praha) MSC: 65C30 60H15 60H35 35R60 35J25 65N30 60G60 PDFBibTeX XMLCite \textit{I. G. Graham} et al., Numer. Math. 131, No. 2, 329--368 (2015; Zbl 1341.65003) Full Text: DOI
Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients. (English) Zbl 1318.65006 Found. Comput. Math. 15, No. 2, 411-449 (2015). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65C30 60H15 60H35 35R60 65C05 65N15 65N55 PDFBibTeX XMLCite \textit{F. Y. Kuo} et al., Found. Comput. Math. 15, No. 2, 411--449 (2015; Zbl 1318.65006) Full Text: DOI arXiv
Dahmen, Wolfgang; Huang, Chunyan; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit Efficient resolution of anisotropic structures. (English) Zbl 1317.65251 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, 25-51 (2014). MSC: 65R20 45K05 PDFBibTeX XMLCite \textit{W. Dahmen} et al., Lect. Notes Comput. Sci. Eng. 102, 25--51 (2014; Zbl 1317.65251) Full Text: DOI arXiv Link
Kornhuber, Ralf; Schwab, Christoph; Wolf, Maren-Wanda Multilevel Monte Carlo finite element methods for stochastic elliptic variational inequalities. (English) Zbl 1320.65176 SIAM J. Numer. Anal. 52, No. 3, 1243-1268 (2014). MSC: 65N30 65C05 65C30 65N55 60H15 65K15 65N75 PDFBibTeX XMLCite \textit{R. Kornhuber} et al., SIAM J. Numer. Anal. 52, No. 3, 1243--1268 (2014; Zbl 1320.65176) Full Text: DOI Link
Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. (English) Zbl 1326.65013 SIAM J. Numer. Anal. 52, No. 6, 2676-2702 (2014). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C05 65D30 65D32 65N30 65N75 35R60 45R05 65C30 60H25 60G60 65J10 PDFBibTeX XMLCite \textit{J. Dick} et al., SIAM J. Numer. Anal. 52, No. 6, 2676--2702 (2014; Zbl 1326.65013) Full Text: DOI arXiv Link
Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. (English) Zbl 1298.65022 Found. Comput. Math. 14, No. 4, 601-633 (2014). Reviewer: Manfred Tasche (Rostock) MSC: 65D05 65N35 35J25 41A05 41A10 41A63 PDFBibTeX XMLCite \textit{A. Chkifa} et al., Found. Comput. Math. 14, No. 4, 601--633 (2014; Zbl 1298.65022) Full Text: DOI HAL
Gittelson, Claude Jeffrey; Andreev, Roman; Schwab, Christoph Optimality of adaptive Galerkin methods for random parabolic partial differential equations. (English) Zbl 1293.35372 J. Comput. Appl. Math. 263, 189-201 (2014). MSC: 35R60 60H35 65C20 65N12 65N22 65J10 47B80 PDFBibTeX XMLCite \textit{C. J. Gittelson} et al., J. Comput. Appl. Math. 263, 189--201 (2014; Zbl 1293.35372) Full Text: DOI
Hoang, Viet Ha; Schwab, Christoph \(N\)-term Wiener chaos approximation rates for elliptic PDEs with lognormal Gaussian random inputs. (English) Zbl 1294.65010 Math. Models Methods Appl. Sci. 24, No. 4, 797-826 (2014). Reviewer: Grigori N. Milstein (Yekaterinburg) MSC: 65C30 60H15 60H35 35R60 35J25 65N30 60G60 PDFBibTeX XMLCite \textit{V. H. Hoang} and \textit{C. Schwab}, Math. Models Methods Appl. Sci. 24, No. 4, 797--826 (2014; Zbl 1294.65010) Full Text: DOI
Lang, Annika; Larsson, Stig; Schwab, Christoph Covariance structure of parabolic stochastic partial differential equations. (English) Zbl 1306.60089 Stoch. Partial Differ. Equ., Anal. Comput. 1, No. 2, 351-364 (2013). MSC: 60H15 35R60 35K70 PDFBibTeX XMLCite \textit{A. Lang} et al., Stoch. Partial Differ. Equ., Anal. Comput. 1, No. 2, 351--364 (2013; Zbl 1306.60089) Full Text: DOI arXiv
Šukys, Jonas; Mishra, Siddhartha; Schwab, Christoph Multi-level Monte Carlo finite difference and finite volume methods for stochastic linear hyperbolic systems. (English) Zbl 1302.65032 Dick, Josef (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2012. Proceedings of the 10th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Sydney, Australia, February 13–17, 2012. Berlin: Springer (ISBN 978-3-642-41094-9/hbk; 978-3-642-41095-6/ebook). Springer Proceedings in Mathematics & Statistics 65, 649-666 (2013). MSC: 65C30 60H15 60H35 35L03 35R60 65C05 65M08 65M06 65Y20 65M15 PDFBibTeX XMLCite \textit{J. Šukys} et al., Springer Proc. Math. Stat. 65, 649--666 (2013; Zbl 1302.65032) Full Text: DOI Link
Schwab, Christoph QMC Galerkin discretization of parametric operator equations. (English) Zbl 1302.65020 Dick, Josef (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2012. Proceedings of the 10th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Sydney, Australia, February 13–17, 2012. Berlin: Springer (ISBN 978-3-642-41094-9/hbk; 978-3-642-41095-6/ebook). Springer Proceedings in Mathematics & Statistics 65, 613-629 (2013). MSC: 65C05 65N30 35J25 35J05 35R60 65N15 PDFBibTeX XMLCite \textit{C. Schwab}, Springer Proc. Math. Stat. 65, 613--629 (2013; Zbl 1302.65020) Full Text: DOI Link
Abdulle, Assyr; Barth, Andrea; Schwab, Christoph Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs. (English) Zbl 1296.65008 Multiscale Model. Simul. 11, No. 4, 1033-1070 (2013). Reviewer: Philipp Dörsek (London) MSC: 65C30 60H15 60H35 35R60 65N30 65C05 65N12 PDFBibTeX XMLCite \textit{A. Abdulle} et al., Multiscale Model. Simul. 11, No. 4, 1033--1070 (2013; Zbl 1296.65008) Full Text: DOI Link
Hoang, Viet Ha; Schwab, Christoph Sparse tensor Galerkin discretization of parametric and random parabolic PDEs—analytic regularity and generalized polynomial chaos approximation. (English) Zbl 1285.35137 SIAM J. Math. Anal. 45, No. 5, 3050-3083 (2013). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35R60 35K20 41A10 41A25 PDFBibTeX XMLCite \textit{V. H. Hoang} and \textit{C. Schwab}, SIAM J. Math. Anal. 45, No. 5, 3050--3083 (2013; Zbl 1285.35137) Full Text: DOI Link
Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. Complexity analysis of accelerated MCMC methods for Bayesian inversion. (English) Zbl 1288.65004 Inverse Probl. 29, No. 8, Article ID 085010, 37 p. (2013). Reviewer: Abass Sagna (Evry) MSC: 65C05 65C40 62F15 65J22 PDFBibTeX XMLCite \textit{V. H. Hoang} et al., Inverse Probl. 29, No. 8, Article ID 085010, 37 p. (2013; Zbl 1288.65004) Full Text: DOI arXiv
Schwab, Christoph; Süli, Endre Adaptive Galerkin approximation algorithms for Kolmogorov equations in infinite dimensions. (English) Zbl 1286.35257 Stoch. Partial Differ. Equ., Anal. Comput. 1, No. 1, 204-239 (2013). Reviewer: Martin Riedler (Wien) MSC: 35R15 35R60 60H15 65C30 PDFBibTeX XMLCite \textit{C. Schwab} and \textit{E. Süli}, Stoch. Partial Differ. Equ., Anal. Comput. 1, No. 1, 204--239 (2013; Zbl 1286.35257) Full Text: DOI
Gittelson, Claude J.; Könnö, Juho; Schwab, Christoph; Stenberg, Rolf The multi-level Monte Carlo finite element method for a stochastic Brinkman problem. (English) Zbl 1281.65010 Numer. Math. 125, No. 2, 347-386 (2013). Reviewer: Abass Sagna (Evry) MSC: 65C30 65C05 60H15 35R60 60H35 35J60 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{C. J. Gittelson} et al., Numer. Math. 125, No. 2, 347--386 (2013; Zbl 1281.65010) Full Text: DOI Link
Kunoth, Angela; Schwab, Christoph Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs. (English) Zbl 1278.49043 SIAM J. Control Optim. 51, No. 3, 2442-2471 (2013). Reviewer: Bülent Karasözen (Ankara) MSC: 49N10 41A29 65K10 65N99 65C30 60H15 PDFBibTeX XMLCite \textit{A. Kunoth} and \textit{C. Schwab}, SIAM J. Control Optim. 51, No. 3, 2442--2471 (2013; Zbl 1278.49043) Full Text: DOI Link
Hansen, Markus; Schwab, Christoph Analytic regularity and nonlinear approximation of a class of parametric semilinear elliptic PDEs. (English) Zbl 1273.35134 Math. Nachr. 286, No. 8-9, 832-860 (2013). MSC: 35J61 35B30 65N30 41A58 PDFBibTeX XMLCite \textit{M. Hansen} and \textit{C. Schwab}, Math. Nachr. 286, No. 8--9, 832--860 (2013; Zbl 1273.35134) Full Text: DOI Link
Chkifa, Abdellah; Cohen, Albert; Devore, Ronald; Schwab, Christoph Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs. (English) Zbl 1273.65009 ESAIM, Math. Model. Numer. Anal. 47, No. 1, 253-280 (2013). Reviewer: Grigori N. Milstein (Yekaterinburg) MSC: 65C30 65N35 35J25 60H15 60H35 35R60 PDFBibTeX XMLCite \textit{A. Chkifa} et al., ESAIM, Math. Model. Numer. Anal. 47, No. 1, 253--280 (2013; Zbl 1273.65009) Full Text: DOI
Barth, Andrea; Lang, Annika; Schwab, Christoph Multilevel Monte Carlo method for parabolic stochastic partial differential equations. (English) Zbl 1272.65009 BIT 53, No. 1, 3-27 (2013). Reviewer: Dominique Lepingle (Orléans) MSC: 65C30 60H15 60H35 65C05 35R60 35K20 65M12 65Y20 PDFBibTeX XMLCite \textit{A. Barth} et al., BIT 53, No. 1, 3--27 (2013; Zbl 1272.65009) Full Text: DOI Link
Hoang, V. H.; Schwab, CH. Analytic regularity and polynomial approximation of stochastic, parametric elliptic multiscale PDEs. (English) Zbl 1259.49059 Anal. Appl., Singap. 11, No. 1, Paper No. 1350001, 50 p. (2013). MSC: 49N60 60H15 35B27 74Q05 65N30 PDFBibTeX XMLCite \textit{V. H. Hoang} and \textit{CH. Schwab}, Anal. Appl., Singap. 11, No. 1, Paper No. 1350001, 50 p. (2013; Zbl 1259.49059) Full Text: DOI
Mishra, Siddhartha; Schwab, Christoph Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data. (English) Zbl 1271.65018 Math. Comput. 81, No. 280, 1979-2018 (2012). Reviewer: Abdallah Bradji (Annaba) MSC: 65C30 65M08 65C05 35L65 60H15 60H35 35R60 PDFBibTeX XMLCite \textit{S. Mishra} and \textit{C. Schwab}, Math. Comput. 81, No. 280, 1979--2018 (2012; Zbl 1271.65018) Full Text: DOI
Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients. (English) Zbl 1271.65017 SIAM J. Numer. Anal. 50, No. 6, 3351-3374 (2012). Reviewer: Gong Guanglu (Beijing) MSC: 65C30 65N30 60H15 35R60 60H35 35J25 65C05 65N15 PDFBibTeX XMLCite \textit{F. Y. Kuo} et al., SIAM J. Numer. Anal. 50, No. 6, 3351--3374 (2012; Zbl 1271.65017) Full Text: DOI Link
Pentenrieder, Bastian; Schwab, Christoph \(hp\)-FEM for second moments of elliptic PDEs with stochastic data. II: Exponential convergence for stationary singular covariance functions. (English) Zbl 1386.65042 Numer. Methods Partial Differ. Equations 28, No. 5, 1527-1557 (2012). MSC: 65C30 65N30 60G60 60H15 60H25 PDFBibTeX XMLCite \textit{B. Pentenrieder} and \textit{C. Schwab}, Numer. Methods Partial Differ. Equations 28, No. 5, 1527--1557 (2012; Zbl 1386.65042) Full Text: DOI
Pentenrieder, Bastian; Schwab, Christoph \(hp\)-FEM for second moments of elliptic PDEs with stochastic data. I. Analytic regularity. (English) Zbl 1386.65041 Numer. Methods Partial Differ. Equations 28, No. 5, 1497-1526 (2012). MSC: 65C30 65N30 60G60 60H15 60H25 PDFBibTeX XMLCite \textit{B. Pentenrieder} and \textit{C. Schwab}, Numer. Methods Partial Differ. Equations 28, No. 5, 1497--1526 (2012; Zbl 1386.65041) Full Text: DOI
Hoang, Viet Ha; Schwab, Christoph Regularity and generalized polynomial chaos approximation of parametric and random second-order hyperbolic partial differential equations. (English) Zbl 1251.35197 Anal. Appl., Singap. 10, No. 3, 295-326 (2012). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35R60 60H15 74H30 74J05 PDFBibTeX XMLCite \textit{V. H. Hoang} and \textit{C. Schwab}, Anal. Appl., Singap. 10, No. 3, 295--326 (2012; Zbl 1251.35197) Full Text: DOI
Marazzina, Daniele; Reichmann, Oleg; Schwab, Christoph \(hp\)-DGFEM for Kolmogorov-Fokker-Planck equations of multivariate Lévy processes. (English) Zbl 1252.65214 Math. Models Methods Appl. Sci. 22, No. 1, 1150005, 37 p. (2012). MSC: 65R20 45K05 60J75 60J60 91B24 91G60 PDFBibTeX XMLCite \textit{D. Marazzina} et al., Math. Models Methods Appl. Sci. 22, No. 1, 1150005, 37 p. (2012; Zbl 1252.65214) Full Text: DOI
Schwab, Christoph; Gittelson, Claude Jeffrey Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs. (English) Zbl 1269.65010 Acta Numerica 20, 291-467 (2011). MSC: 65C30 60H35 35R60 60H15 PDFBibTeX XMLCite \textit{C. Schwab} and \textit{C. J. Gittelson}, Acta Numerica 20, 291--467 (2011; Zbl 1269.65010) Full Text: DOI
Khoromskij, Boris N.; Schwab, Christoph Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. (English) Zbl 1243.65009 SIAM J. Sci. Comput. 33, No. 1, 364-385 (2011). Reviewer: Kevin Burrage (Brisbane) MSC: 65C30 65F30 65F50 65N35 60H15 60H35 35R60 65F08 PDFBibTeX XMLCite \textit{B. N. Khoromskij} and \textit{C. Schwab}, SIAM J. Sci. Comput. 33, No. 1, 364--385 (2011; Zbl 1243.65009) Full Text: DOI Link
Barth, Andrea; Schwab, Christoph; Zollinger, Nathaniel Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients. (English) Zbl 1230.65006 Numer. Math. 119, No. 1, 123-161 (2011). Reviewer: Grigori N. Milstein (Yekaterinburg) MSC: 65C30 60H15 60H35 35R60 65C05 65Y20 PDFBibTeX XMLCite \textit{A. Barth} et al., Numer. Math. 119, No. 1, 123--161 (2011; Zbl 1230.65006) Full Text: DOI Link
Bieri, Marcel; Andreev, Roman; Schwab, Christoph Convergence rates of sparse tensor GPC FEM for elliptic sPDEs. (English) Zbl 1216.65005 Hesthaven, Jan S. (ed.) et al., Spectral and high order methods for partial differential equations. Selected papers from the 8th ICOSAHOM ’09 conference, Trondheim, Norway, June 22–26, 2009. Berlin: Springer (ISBN 978-3-642-15336-5/hbk; 978-3-642-15337-2/ebook). Lecture Notes in Computational Science and Engineering 76, 101-110 (2011). MSC: 65C30 60H15 60H35 35R60 35J25 65N30 65N12 PDFBibTeX XMLCite \textit{M. Bieri} et al., Lect. Notes Comput. Sci. Eng. 76, 101--110 (2011; Zbl 1216.65005) Full Text: DOI
Cohen, Albert; DeVore, Ronald; Schwab, Christoph Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE’s. (English) Zbl 1219.35379 Anal. Appl., Singap. 9, No. 1, 11-47 (2011). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35R60 60H35 65M20 PDFBibTeX XMLCite \textit{A. Cohen} et al., Anal. Appl., Singap. 9, No. 1, 11--47 (2011; Zbl 1219.35379) Full Text: DOI
Reich, N.; Schwab, C.; Winter, C. On Kolmogorov equations for anisotropic multivariate Lévy processes. (English) Zbl 1226.91092 Finance Stoch. 14, No. 4, 527-567 (2010). MSC: 91G80 91G20 60J75 65M60 45K05 PDFBibTeX XMLCite \textit{N. Reich} et al., Finance Stoch. 14, No. 4, 527--567 (2010; Zbl 1226.91092) Full Text: DOI Link
Cohen, Albert; DeVore, Ronald; Schwab, Christoph Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs. (English) Zbl 1206.60064 Found. Comput. Math. 10, No. 6, 615-646 (2010). MSC: 60H35 65C30 60H15 35R60 PDFBibTeX XMLCite \textit{A. Cohen} et al., Found. Comput. Math. 10, No. 6, 615--646 (2010; Zbl 1206.60064) Full Text: DOI
Bieri, Marcel; Andreev, Roman; Schwab, Christoph Sparse tensor discretization of elliptic SPDEs. (English) Zbl 1205.35346 SIAM J. Sci. Comput. 31, No. 6, 4281-4304 (2009). MSC: 35R60 60H15 65C20 65N12 65N15 65N30 65C05 PDFBibTeX XMLCite \textit{M. Bieri} et al., SIAM J. Sci. Comput. 31, No. 6, 4281--4304 (2009; Zbl 1205.35346) Full Text: DOI
Schwab, Christoph; Stevenson, Rob Space-time adaptive wavelet methods for parabolic evolution problems. (English) Zbl 1198.65249 Math. Comput. 78, No. 267, 1293-1318 (2009). MSC: 65N99 65T60 35K10 41A25 46B28 PDFBibTeX XMLCite \textit{C. Schwab} and \textit{R. Stevenson}, Math. Comput. 78, No. 267, 1293--1318 (2009; Zbl 1198.65249) Full Text: DOI
Bieri, Marcel; Schwab, Christoph Sparse high order FEM for elliptic sPDEs. (English) Zbl 1157.65481 Comput. Methods Appl. Mech. Eng. 198, No. 13-14, 1149-1170 (2009). MSC: 65N30 60H15 PDFBibTeX XMLCite \textit{M. Bieri} and \textit{C. Schwab}, Comput. Methods Appl. Mech. Eng. 198, No. 13--14, 1149--1170 (2009; Zbl 1157.65481) Full Text: DOI
Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph Multilevel frames for sparse tensor product spaces. (English) Zbl 1151.65010 Numer. Math. 110, No. 2, 199-220 (2008). Reviewer: Dominique Lepingle (Orléans) MSC: 65C30 35J25 35R60 65N30 65N55 65T60 60H15 60H35 65N12 PDFBibTeX XMLCite \textit{H. Harbrecht} et al., Numer. Math. 110, No. 2, 199--220 (2008; Zbl 1151.65010) Full Text: DOI
Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph Sparse second moment analysis for elliptic problems in stochastic domains. (English) Zbl 1146.65007 Numer. Math. 109, No. 3, 385-414 (2008). Reviewer: Grigori N. Milstein (Ekaterinburg) MSC: 65C30 35R60 65N38 60H15 60H35 65T60 PDFBibTeX XMLCite \textit{H. Harbrecht} et al., Numer. Math. 109, No. 3, 385--414 (2008; Zbl 1146.65007) Full Text: DOI
Todor, Radu Alexandru; Schwab, Christoph Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients. (English) Zbl 1120.65004 IMA J. Numer. Anal. 27, No. 2, 232-261 (2007). Reviewer: Grigori N. Milstein (Ekaterinburg) MSC: 65C30 60H15 35R60 60H35 65N30 65N35 PDFBibTeX XMLCite \textit{R. A. Todor} and \textit{C. Schwab}, IMA J. Numer. Anal. 27, No. 2, 232--261 (2007; Zbl 1120.65004) Full Text: DOI Link
von Petersdorff, Tobias; Schwab, Christoph Sparse finite element methods for operator equations with stochastic data. (English) Zbl 1164.65300 Appl. Math., Praha 51, No. 2, 145-180 (2006). MSC: 65C05 65N30 60H25 60H15 65C30 65T60 65F10 65F35 PDFBibTeX XMLCite \textit{T. von Petersdorff} and \textit{C. Schwab}, Appl. Math., Praha 51, No. 2, 145--180 (2006; Zbl 1164.65300) Full Text: DOI EuDML Link
Negreanu, Mihaela; Matache, Ana-Maria; Schwab, Christoph Wavelet filtering for exact controllability of the wave equation. (English) Zbl 1131.65056 SIAM J. Sci. Comput. 28, No. 5, 1851-1885 (2006). Reviewer: Nicholas Karampetakis (Thessaloniki) MSC: 65K10 35L05 93B05 93B07 93C20 65M60 65M55 PDFBibTeX XMLCite \textit{M. Negreanu} et al., SIAM J. Sci. Comput. 28, No. 5, 1851--1885 (2006; Zbl 1131.65056) Full Text: DOI
Schwab, Christoph; Todor, Radu Alexandru Karhunen-Loève approximation of random fields by generalized fast multipole methods. (English) Zbl 1104.65008 J. Comput. Phys. 217, No. 1, 100-122 (2006). Reviewer: Silvia Curteanu (Iaşi) MSC: 65C50 65M60 60G60 65C30 60H15 65N25 PDFBibTeX XMLCite \textit{C. Schwab} and \textit{R. A. Todor}, J. Comput. Phys. 217, No. 1, 100--122 (2006; Zbl 1104.65008) Full Text: DOI
Matache, Ana-Maria; Schwab, Christoph; Wihler, Thomas P. Linear complexity solution of parabolic integro-differential equations. (English) Zbl 1102.65139 Numer. Math. 104, No. 1, 69-102 (2006). Reviewer: Neville Ford (Chester) MSC: 65R20 45K05 35S10 91G60 PDFBibTeX XMLCite \textit{A.-M. Matache} et al., Numer. Math. 104, No. 1, 69--102 (2006; Zbl 1102.65139) Full Text: DOI Link
Matache, Ana-Maria; Schwab, Christoph; Wihler, Thomas P. Fast numerical solution of parabolic integro-differential equations with applications in finance. (English) Zbl 1098.65123 SIAM J. Sci. Comput. 27, No. 2, 369-393 (2005). Reviewer: Lechoslaw Hącia (Poznań) MSC: 65R20 45K05 60J75 65T60 91G60 PDFBibTeX XMLCite \textit{A.-M. Matache} et al., SIAM J. Sci. Comput. 27, No. 2, 369--393 (2005; Zbl 1098.65123) Full Text: DOI
Frauenfelder, Philipp; Schwab, Christoph; Todor, Radu Alexandru Finite elements for elliptic problems with stochastic coefficients. (English) Zbl 1143.65392 Comput. Methods Appl. Mech. Eng. 194, No. 2-5, 205-228 (2005). MSC: 65N30 60H15 60H35 PDFBibTeX XMLCite \textit{P. Frauenfelder} et al., Comput. Methods Appl. Mech. Eng. 194, No. 2--5, 205--228 (2005; Zbl 1143.65392) Full Text: DOI
von Petersdorff, Tobias; Schwab, Christoph Numerical solution of parabolic equations in high dimensions. (English) Zbl 1083.65095 M2AN, Math. Model. Numer. Anal. 38, No. 1, 93-127 (2004). Reviewer: Kai Schneider (Marseille) MSC: 65M60 35K90 35K05 65M12 65M15 PDFBibTeX XMLCite \textit{T. von Petersdorff} and \textit{C. Schwab}, M2AN, Math. Model. Numer. Anal. 38, No. 1, 93--127 (2004; Zbl 1083.65095) Full Text: DOI Numdam EuDML
Matache, Ana-Maria; von Petersdorff, Tobias; Schwab, Christoph Fast deterministic pricing of options on Lévy driven assets. (English) Zbl 1072.60052 M2AN, Math. Model. Numer. Anal. 38, No. 1, 37-71 (2004). MSC: 60H30 60G51 60H15 60J75 65M60 65T60 91G20 PDFBibTeX XMLCite \textit{A.-M. Matache} et al., M2AN, Math. Model. Numer. Anal. 38, No. 1, 37--71 (2004; Zbl 1072.60052) Full Text: DOI Numdam EuDML
von Petersdorff, Tobias; Schwab, Christoph Wavelet discretizations of parabolic integrodifferential equations. (English) Zbl 1050.65134 SIAM J. Numer. Anal. 41, No. 1, 159-180 (2003). Reviewer: Chaman Lal Koul (Jaipur) MSC: 65R20 45K05 65T60 PDFBibTeX XMLCite \textit{T. von Petersdorff} and \textit{C. Schwab}, SIAM J. Numer. Anal. 41, No. 1, 159--180 (2003; Zbl 1050.65134) Full Text: DOI
Schwab, Christoph; Todor, Radu-Alexandru Sparse finite elements for elliptic problems with stochastic loading. (English) Zbl 1044.65085 Numer. Math. 95, No. 4, 707-734 (2003). Reviewer: Michel Bernadou (Paris La Defense) MSC: 65N30 65C30 35J25 60H15 35R60 65C05 65N12 65F10 65F35 65N55 PDFBibTeX XMLCite \textit{C. Schwab} and \textit{R.-A. Todor}, Numer. Math. 95, No. 4, 707--734 (2003; Zbl 1044.65085) Full Text: DOI Link
Schwab, Ch.; Todor, R. A. Sparse finite elements for stochastic elliptic problems — higher order moments. (English) Zbl 1044.65006 Computing 71, No. 1, 43-63 (2003). Reviewer: Eckhard Platen (Broadway) MSC: 65C30 65N30 60H15 35R60 35J25 65N50 60H35 65T60 PDFBibTeX XMLCite \textit{Ch. Schwab} and \textit{R. A. Todor}, Computing 71, No. 1, 43--63 (2003; Zbl 1044.65006) Full Text: DOI Link
Matache, Ana-Maria; Roubíček, Tomáš; Schwab, Christoph Higher-order convex approximations of Young measures in optimal control. (English) Zbl 1027.65086 Adv. Comput. Math. 19, No. 1-3, 73-97 (2003). Reviewer: Asaf D.Iskenderov (Baku) MSC: 65K10 49J20 49M25 PDFBibTeX XMLCite \textit{A.-M. Matache} et al., Adv. Comput. Math. 19, No. 1--3, 73--97 (2003; Zbl 1027.65086) Full Text: DOI
Schwab, Christoph Higher dimensional finite elements for elliptic problems with multiple scales and stochastic data. (English) Zbl 1001.65120 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press. 727-734 (2002). MSC: 65N30 60H15 35R60 65C30 35B27 35J25 65T60 PDFBibTeX XMLCite \textit{C. Schwab}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 727--734 (2002; Zbl 1001.65120) Full Text: arXiv
Schwab, Christoph; Wendland, Wolfgang L. Kernel properties and representations of boundary integral operators. (English) Zbl 0805.35168 Math. Nachr. 156, 187-218 (1992). MSC: 35S05 35J30 31B10 PDFBibTeX XMLCite \textit{C. Schwab} and \textit{W. L. Wendland}, Math. Nachr. 156, 187--218 (1992; Zbl 0805.35168) Full Text: DOI