Karner, Clemens; Kazeev, Vladimir; Petersen, Philipp Christian Limitations of neural network training due to numerical instability of backpropagation. (English) Zbl 07811923 Adv. Comput. Math. 50, No. 1, Paper No. 14, 33 p. (2024). MSC: 65G99 68T07 35A18 PDFBibTeX XMLCite \textit{C. Karner} et al., Adv. Comput. Math. 50, No. 1, Paper No. 14, 33 p. (2024; Zbl 07811923) Full Text: DOI arXiv OA License
Çiloğlu, Pelin; Yücel, Hamdullah Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients. (English) Zbl 07667232 Adv. Comput. Math. 49, No. 2, Paper No. 16, 36 p. (2023). MSC: 65-XX 35R60 49J20 60H15 60H35 PDFBibTeX XMLCite \textit{P. Çiloğlu} and \textit{H. Yücel}, Adv. Comput. Math. 49, No. 2, Paper No. 16, 36 p. (2023; Zbl 07667232) Full Text: DOI arXiv
Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; Zimmermann, Philipp Space-time error estimates for deep neural network approximations for differential equations. (English) Zbl 07649348 Adv. Comput. Math. 49, No. 1, Paper No. 4, 78 p. (2023). MSC: 65-XX PDFBibTeX XMLCite \textit{P. Grohs} et al., Adv. Comput. Math. 49, No. 1, Paper No. 4, 78 p. (2023; Zbl 07649348) Full Text: DOI arXiv
Hubbert, Simon; Jäger, Janin Generalised Wendland functions for the sphere. (English) Zbl 07642011 Adv. Comput. Math. 49, No. 1, Paper No. 3, 21 p. (2023). MSC: 42A16 42A82 42C10 33C55 41A05 41A25 PDFBibTeX XMLCite \textit{S. Hubbert} and \textit{J. Jäger}, Adv. Comput. Math. 49, No. 1, Paper No. 3, 21 p. (2023; Zbl 07642011) Full Text: DOI arXiv
De Ryck, Tim; Mishra, Siddhartha Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs. (English) Zbl 1502.65170 Adv. Comput. Math. 48, No. 6, Paper No. 79, 40 p. (2022). MSC: 65M99 68T07 65M15 35K55 35K05 91G20 35Q53 PDFBibTeX XMLCite \textit{T. De Ryck} and \textit{S. Mishra}, Adv. Comput. Math. 48, No. 6, Paper No. 79, 40 p. (2022; Zbl 1502.65170) Full Text: DOI arXiv
Jiang, Nan; Yang, Huanhuan Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier-Stokes equations. (English) Zbl 07608423 Adv. Comput. Math. 48, No. 5, Paper No. 65, 30 p. (2022). MSC: 65Mxx 65M12 65M60 76D05 PDFBibTeX XMLCite \textit{N. Jiang} and \textit{H. Yang}, Adv. Comput. Math. 48, No. 5, Paper No. 65, 30 p. (2022; Zbl 07608423) Full Text: DOI
Faustmann, Markus; Melenk, Jens Markus; Parvizi, Maryam \({\mathcal{H}} \)-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations. (English) Zbl 1502.65199 Adv. Comput. Math. 48, No. 5, Paper No. 59, 32 p. (2022). MSC: 65N30 65F55 78A25 35Q61 PDFBibTeX XMLCite \textit{M. Faustmann} et al., Adv. Comput. Math. 48, No. 5, Paper No. 59, 32 p. (2022; Zbl 1502.65199) Full Text: DOI arXiv
Ding, Qianqian; Mao, Shipeng; Sun, Jiaao Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system. (English) Zbl 1498.76052 Adv. Comput. Math. 48, No. 5, Paper No. 55, 23 p. (2022). MSC: 76M10 76W05 65M15 65M12 PDFBibTeX XMLCite \textit{Q. Ding} et al., Adv. Comput. Math. 48, No. 5, Paper No. 55, 23 p. (2022; Zbl 1498.76052) Full Text: DOI
Congreve, Scott; Houston, Paul Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes. (English) Zbl 1497.35226 Adv. Comput. Math. 48, No. 5, Paper No. 54, 31 p. (2022). MSC: 35J62 35J25 65N30 PDFBibTeX XMLCite \textit{S. Congreve} and \textit{P. Houston}, Adv. Comput. Math. 48, No. 5, Paper No. 54, 31 p. (2022; Zbl 1497.35226) Full Text: DOI arXiv
Marchand, P.; Galkowski, J.; Spence, E. A.; Spence, A. Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency? (English) Zbl 1492.65090 Adv. Comput. Math. 48, No. 4, Paper No. 37, 63 p. (2022). MSC: 65F10 65N22 35J05 65N38 PDFBibTeX XMLCite \textit{P. Marchand} et al., Adv. Comput. Math. 48, No. 4, Paper No. 37, 63 p. (2022; Zbl 1492.65090) Full Text: DOI arXiv
Marcati, C.; Rakhuba, M.; Schwab, Ch. Tensor rank bounds for point singularities in \(\mathbb{R}^3\). (English) Zbl 1487.35019 Adv. Comput. Math. 48, No. 3, Paper No. 18, 57 p. (2022). MSC: 35A35 15A69 35J15 41A25 41A46 65N30 PDFBibTeX XMLCite \textit{C. Marcati} et al., Adv. Comput. Math. 48, No. 3, Paper No. 18, 57 p. (2022; Zbl 1487.35019) Full Text: DOI arXiv
Stevenson, Rob; van Venetië, Raymond; Westerdiep, Jan A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations. (English) Zbl 07506442 Adv. Comput. Math. 48, No. 3, Paper No. 17, 43 p. (2022). MSC: 65-XX 35K20 65F08 65M12 65M60 65T60 PDFBibTeX XMLCite \textit{R. Stevenson} et al., Adv. Comput. Math. 48, No. 3, Paper No. 17, 43 p. (2022; Zbl 07506442) Full Text: DOI arXiv
Kleefeld, Andreas The hot spots conjecture can be false: some numerical examples. (English) Zbl 1487.35204 Adv. Comput. Math. 47, No. 6, Paper No. 85, 31 p. (2021). Reviewer: Gilles Evéquoz (Delémont) MSC: 35J25 35P20 65F15 65M38 PDFBibTeX XMLCite \textit{A. Kleefeld}, Adv. Comput. Math. 47, No. 6, Paper No. 85, 31 p. (2021; Zbl 1487.35204) Full Text: DOI arXiv
Muoi, Pham Quy; Tan, Wee Chin; Hoang, Viet Ha Essentially optimal finite elements for multiscale elliptic eigenvalue problems. (English) Zbl 1479.65030 Adv. Comput. Math. 47, No. 6, Paper No. 80, 25 p. (2021). MSC: 65N30 65N25 65N15 35P15 35B27 35B65 35J15 PDFBibTeX XMLCite \textit{P. Q. Muoi} et al., Adv. Comput. Math. 47, No. 6, Paper No. 80, 25 p. (2021; Zbl 1479.65030) Full Text: DOI
Liu, Wenjie; Wang, Li-Lian; Wu, Boying Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation. (English) Zbl 1496.41003 Adv. Comput. Math. 47, No. 6, Paper No. 79, 32 p. (2021). Reviewer: Zoltán Finta (Cluj-Napoca) MSC: 41A10 41A25 41A44 65N35 PDFBibTeX XMLCite \textit{W. Liu} et al., Adv. Comput. Math. 47, No. 6, Paper No. 79, 32 p. (2021; Zbl 1496.41003) Full Text: DOI arXiv
Elasmi, Mehdi; Erath, Christoph; Kurz, Stefan Non-symmetric isogeometric FEM-BEM couplings. (English) Zbl 1491.65133 Adv. Comput. Math. 47, No. 5, Paper No. 61, 36 p. (2021). MSC: 65N30 65N38 65N12 65N15 65D07 35A01 35A02 35B45 78A55 78M10 78M15 PDFBibTeX XMLCite \textit{M. Elasmi} et al., Adv. Comput. Math. 47, No. 5, Paper No. 61, 36 p. (2021; Zbl 1491.65133) Full Text: DOI arXiv
Graham, I. G.; Pembery, O. R.; Spence, E. A. Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification. (English) Zbl 1473.35122 Adv. Comput. Math. 47, No. 5, Paper No. 68, 39 p. (2021). MSC: 35J05 35J25 65F08 65N22 65N30 PDFBibTeX XMLCite \textit{I. G. Graham} et al., Adv. Comput. Math. 47, No. 5, Paper No. 68, 39 p. (2021; Zbl 1473.35122) Full Text: DOI arXiv
Atkinson, Kendall; Chien, David; Hansen, Olaf Multivariate quadrature of a singular integrand. (English) Zbl 1472.65032 Adv. Comput. Math. 47, No. 3, Paper No. 44, 27 p. (2021). MSC: 65D32 65D30 PDFBibTeX XMLCite \textit{K. Atkinson} et al., Adv. Comput. Math. 47, No. 3, Paper No. 44, 27 p. (2021; Zbl 1472.65032) Full Text: DOI
Castrillón-Candás, Julio E.; Nobile, Fabio; Tempone, Raúl F. A hybrid collocation-perturbation approach for PDEs with random domains. (English) Zbl 1479.65033 Adv. Comput. Math. 47, No. 3, Paper No. 40, 35 p. (2021). MSC: 65N35 65N30 65N12 35B20 35R60 PDFBibTeX XMLCite \textit{J. E. Castrillón-Candás} et al., Adv. Comput. Math. 47, No. 3, Paper No. 40, 35 p. (2021; Zbl 1479.65033) Full Text: DOI arXiv
Ye, Xiu; Zhang, Shangyou A stabilizer-free pressure-robust finite element method for the Stokes equations. (English) Zbl 1473.65323 Adv. Comput. Math. 47, No. 2, Paper No. 28, 17 p. (2021). MSC: 65N30 65N15 76D07 76M10 35Q35 PDFBibTeX XMLCite \textit{X. Ye} and \textit{S. Zhang}, Adv. Comput. Math. 47, No. 2, Paper No. 28, 17 p. (2021; Zbl 1473.65323) Full Text: DOI arXiv
Chernov, A.; Marcati, C.; Mascotto, L. \(p\)- and \(hp\)-virtual elements for the Stokes problem. (English) Zbl 1475.65187 Adv. Comput. Math. 47, No. 2, Paper No. 24, 31 p. (2021). Reviewer: Marius Ghergu (Dublin) MSC: 65N30 65N12 65N15 76D07 PDFBibTeX XMLCite \textit{A. Chernov} et al., Adv. Comput. Math. 47, No. 2, Paper No. 24, 31 p. (2021; Zbl 1475.65187) Full Text: DOI arXiv
Laakmann, Fabian; Petersen, Philipp Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs. (English) Zbl 1472.65134 Adv. Comput. Math. 47, No. 1, Paper No. 11, 32 p. (2021). MSC: 65M99 35A35 68T07 35Q49 92B20 PDFBibTeX XMLCite \textit{F. Laakmann} and \textit{P. Petersen}, Adv. Comput. Math. 47, No. 1, Paper No. 11, 32 p. (2021; Zbl 1472.65134) Full Text: DOI arXiv
Bochmann, Maximilian; Kämmerer, Lutz; Potts, Daniel A sparse FFT approach for ODE with random coefficients. (English) Zbl 1455.65241 Adv. Comput. Math. 46, No. 5, Paper No. 65, 21 p. (2020). MSC: 65T50 65C30 42A10 60H10 60H35 PDFBibTeX XMLCite \textit{M. Bochmann} et al., Adv. Comput. Math. 46, No. 5, Paper No. 65, 21 p. (2020; Zbl 1455.65241) Full Text: DOI arXiv
Ali, Mazen; Urban, Karsten HT-AWGM: a hierarchical Tucker-adaptive wavelet Galerkin method for high-dimensional elliptic problems. (English) Zbl 1454.65158 Adv. Comput. Math. 46, No. 4, Paper No. 59, 34 p. (2020). MSC: 65N30 65T60 65F08 65F10 15A72 PDFBibTeX XMLCite \textit{M. Ali} and \textit{K. Urban}, Adv. Comput. Math. 46, No. 4, Paper No. 59, 34 p. (2020; Zbl 1454.65158) Full Text: DOI arXiv
Wei, Yichen; Yi, Lijun An \(hp\)-version of the \(C^0\)-continuous Petrov-Galerkin time stepping method for nonlinear second-order initial value problems. (English) Zbl 1441.65068 Adv. Comput. Math. 46, No. 4, Paper No. 56, 25 p. (2020). MSC: 65L60 65L05 65L70 PDFBibTeX XMLCite \textit{Y. Wei} and \textit{L. Yi}, Adv. Comput. Math. 46, No. 4, Paper No. 56, 25 p. (2020; Zbl 1441.65068) Full Text: DOI
Wang, Haiyong; Zhang, Lun Analysis of multivariate Gegenbauer approximation in the hypercube. (English) Zbl 1441.41002 Adv. Comput. Math. 46, No. 4, Paper No. 53, 29 p. (2020). Reviewer: Martin D. Buhmann (Gießen) MSC: 41A10 41A25 41A63 PDFBibTeX XMLCite \textit{H. Wang} and \textit{L. Zhang}, Adv. Comput. Math. 46, No. 4, Paper No. 53, 29 p. (2020; Zbl 1441.41002) Full Text: DOI arXiv
Leng, Haitao; Chen, Yanping Adaptive hybridizable discontinuous Galerkin methods for nonstationary convection diffusion problems. (English) Zbl 1442.65265 Adv. Comput. Math. 46, No. 4, Paper No. 50, 23 p. (2020). MSC: 65M60 65M15 65M22 65M06 PDFBibTeX XMLCite \textit{H. Leng} and \textit{Y. Chen}, Adv. Comput. Math. 46, No. 4, Paper No. 50, 23 p. (2020; Zbl 1442.65265) Full Text: DOI
Bonizzoni, Francesca; Nobile, Fabio; Perugia, Ilaria; Pradovera, Davide Least-squares Padé approximation of parametric and stochastic Helmholtz maps. (English) Zbl 1439.30058 Adv. Comput. Math. 46, No. 3, Paper No. 46, 28 p. (2020). MSC: 30E10 35J05 41A21 32K12 PDFBibTeX XMLCite \textit{F. Bonizzoni} et al., Adv. Comput. Math. 46, No. 3, Paper No. 46, 28 p. (2020; Zbl 1439.30058) Full Text: DOI arXiv
Grohs, Philipp; Kutyniok, Gitta; Ma, Jackie; Petersen, Philipp; Raslan, Mones Anisotropic multiscale systems on bounded domains. (English) Zbl 1442.42076 Adv. Comput. Math. 46, No. 2, Paper No. 39, 33 p. (2020). Reviewer: Yankui Sun (Beijing) MSC: 42C40 65M60 41A25 46E36 65T99 94A11 PDFBibTeX XMLCite \textit{P. Grohs} et al., Adv. Comput. Math. 46, No. 2, Paper No. 39, 33 p. (2020; Zbl 1442.42076) Full Text: DOI arXiv
Li, Rui; Gao, Yali; Chen, Jie; Zhang, Li; He, Xiaoming; Chen, Zhangxin Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model. (English) Zbl 1436.65125 Adv. Comput. Math. 46, No. 2, Paper No. 25, 35 p. (2020). MSC: 65M08 65M60 65M50 65M12 76D05 76D45 76T06 76M12 35Q35 PDFBibTeX XMLCite \textit{R. Li} et al., Adv. Comput. Math. 46, No. 2, Paper No. 25, 35 p. (2020; Zbl 1436.65125) Full Text: DOI
Kuehn, Christian; Kürschner, Patrick Combined error estimates for local fluctuations of SPDEs. (English) Zbl 07189697 Adv. Comput. Math. 46, No. 1, Paper No. 11, 25 p. (2020). MSC: 65C30 65M99 60H15 35R60 37M99 15A24 PDFBibTeX XMLCite \textit{C. Kuehn} and \textit{P. Kürschner}, Adv. Comput. Math. 46, No. 1, Paper No. 11, 25 p. (2020; Zbl 07189697) Full Text: DOI arXiv
Karkulik, Michael; Melenk, Jens Markus \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian. (English) Zbl 1435.65205 Adv. Comput. Math. 45, No. 5-6, 2893-2919 (2019). MSC: 65N30 65F05 65F50 26A33 35R11 PDFBibTeX XMLCite \textit{M. Karkulik} and \textit{J. M. Melenk}, Adv. Comput. Math. 45, No. 5--6, 2893--2919 (2019; Zbl 1435.65205) Full Text: DOI arXiv
Eigel, Martin; Schneider, Reinhold; Trunschke, Philipp; Wolf, Sebastian Variational Monte Carlo – bridging concepts of machine learning and high-dimensional partial differential equations. (English) Zbl 1435.68258 Adv. Comput. Math. 45, No. 5-6, 2503-2532 (2019). MSC: 68T05 15A69 35R60 62J02 65C05 65D15 65N22 65N30 PDFBibTeX XMLCite \textit{M. Eigel} et al., Adv. Comput. Math. 45, No. 5--6, 2503--2532 (2019; Zbl 1435.68258) Full Text: DOI arXiv
Peherstorfer, Benjamin; Marzouk, Youssef A transport-based multifidelity preconditioner for Markov chain Monte Carlo. (English) Zbl 07179095 Adv. Comput. Math. 45, No. 5-6, 2321-2348 (2019). MSC: 65C05 65C40 65C60 PDFBibTeX XMLCite \textit{B. Peherstorfer} and \textit{Y. Marzouk}, Adv. Comput. Math. 45, No. 5--6, 2321--2348 (2019; Zbl 07179095) Full Text: DOI arXiv Link
Hain, Stefan; Ohlberger, Mario; Radic, Mladjan; Urban, Karsten A hierarchical a posteriori error estimator for the reduced basis method. (English) Zbl 1435.65203 Adv. Comput. Math. 45, No. 5-6, 2191-2214 (2019). MSC: 65N30 65N15 35J05 PDFBibTeX XMLCite \textit{S. Hain} et al., Adv. Comput. Math. 45, No. 5--6, 2191--2214 (2019; Zbl 1435.65203) Full Text: DOI arXiv
Wang, Wansheng Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay. (English) Zbl 1415.65149 Adv. Comput. Math. 45, No. 3, 1631-1655 (2019). MSC: 65L03 65L06 65L20 PDFBibTeX XMLCite \textit{W. Wang}, Adv. Comput. Math. 45, No. 3, 1631--1655 (2019; Zbl 1415.65149) Full Text: DOI
Petersen, Philipp; Raslan, Mones Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces. (English) Zbl 1422.42049 Adv. Comput. Math. 45, No. 3, 1581-1606 (2019). Reviewer: Nikhil Khanna (New Delhi) MSC: 42C40 65M60 41A25 65T99 94A12 PDFBibTeX XMLCite \textit{P. Petersen} and \textit{M. Raslan}, Adv. Comput. Math. 45, No. 3, 1581--1606 (2019; Zbl 1422.42049) Full Text: DOI arXiv
Tan, Wee Chin; Hoang, Viet Ha High dimensional finite elements for time-space multiscale parabolic equations. (English) Zbl 1419.65071 Adv. Comput. Math. 45, No. 3, 1291-1327 (2019). MSC: 65M60 65M12 35B27 35C20 PDFBibTeX XMLCite \textit{W. C. Tan} and \textit{V. H. Hoang}, Adv. Comput. Math. 45, No. 3, 1291--1327 (2019; Zbl 1419.65071) Full Text: DOI
Rekatsinas, Nikolaos; Stevenson, Rob An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems. (English) Zbl 1415.65294 Adv. Comput. Math. 45, No. 2, 1031-1066 (2019). MSC: 65T60 65N30 35K20 41A25 41A63 42C40 65N12 PDFBibTeX XMLCite \textit{N. Rekatsinas} and \textit{R. Stevenson}, Adv. Comput. Math. 45, No. 2, 1031--1066 (2019; Zbl 1415.65294) Full Text: DOI
Dong, Zhaonan On the exponent of exponential convergence of \(p\)-version FEM spaces. (English) Zbl 1415.65253 Adv. Comput. Math. 45, No. 2, 757-785 (2019). MSC: 65N30 65N15 65N50 PDFBibTeX XMLCite \textit{Z. Dong}, Adv. Comput. Math. 45, No. 2, 757--785 (2019; Zbl 1415.65253) Full Text: DOI arXiv
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
Wang, Lina; Yi, Lijun An \(h\)-\(p\) version of the continuous Petrov-Galerkin method for Volterra delay-integro-differential equations. (English) Zbl 1387.65077 Adv. Comput. Math. 43, No. 6, 1437-1467 (2017). MSC: 65L60 65L05 65R20 65L70 PDFBibTeX XMLCite \textit{L. Wang} and \textit{L. Yi}, Adv. Comput. Math. 43, No. 6, 1437--1467 (2017; Zbl 1387.65077) Full Text: DOI
Claeys, X.; Hiptmair, R.; Spindler, Elke Second kind boundary integral equation for multi-subdomain diffusion problems. (English) Zbl 1381.65094 Adv. Comput. Math. 43, No. 5, 1075-1101 (2017). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N38 65N12 35J05 PDFBibTeX XMLCite \textit{X. Claeys} et al., Adv. Comput. Math. 43, No. 5, 1075--1101 (2017; Zbl 1381.65094) Full Text: DOI HAL
Cao, Yanzhao; Jiang, Ying; Xu, Yuesheng A fast discrete spectral method for stochastic partial differential equations. (English) Zbl 1386.60213 Adv. Comput. Math. 43, No. 5, 973-998 (2017). MSC: 60H15 41A63 78M22 PDFBibTeX XMLCite \textit{Y. Cao} et al., Adv. Comput. Math. 43, No. 5, 973--998 (2017; Zbl 1386.60213) Full Text: DOI
Kazeev, Vladimir; Oseledets, Ivan; Rakhuba, Maxim; Schwab, Christoph QTT-finite-element approximation for multiscale problems. I: Model problems in one dimension. (English) Zbl 1375.65152 Adv. Comput. Math. 43, No. 2, 411-442 (2017). Reviewer: Maria Gousidou-Koutita (Thessaloniki) MSC: 65N30 15A69 35B27 35J05 65N15 65N12 PDFBibTeX XMLCite \textit{V. Kazeev} et al., Adv. Comput. Math. 43, No. 2, 411--442 (2017; Zbl 1375.65152) Full Text: DOI
Ali, Mazen; Steih, Kristina; Urban, Karsten Reduced basis methods with adaptive snapshot computations. (English) Zbl 1379.65087 Adv. Comput. Math. 43, No. 2, 257-294 (2017). Reviewer: Petr Sváček (Praha) MSC: 65N30 35B10 65Y20 65N15 65N12 PDFBibTeX XMLCite \textit{M. Ali} et al., Adv. Comput. Math. 43, No. 2, 257--294 (2017; Zbl 1379.65087) Full Text: DOI arXiv
Choi, Young Ok; Tausch, Johannes The Galerkin boundary element method for transient Stokes flow. (English) Zbl 1368.76044 Adv. Comput. Math. 43, No. 3, 473-493 (2017). MSC: 76M15 76D07 PDFBibTeX XMLCite \textit{Y. O. Choi} and \textit{J. Tausch}, Adv. Comput. Math. 43, No. 3, 473--493 (2017; Zbl 1368.76044) Full Text: DOI
Tian, Xiaochuan; Du, Qiang; Gunzburger, Max Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. (English) Zbl 1356.65239 Adv. Comput. Math. 42, No. 6, 1363-1380 (2016). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 35R11 35J05 65N12 PDFBibTeX XMLCite \textit{X. Tian} et al., Adv. Comput. Math. 42, No. 6, 1363--1380 (2016; Zbl 1356.65239) Full Text: DOI
Redeker, Magnus; Haasdonk, Bernard A POD-EIM reduced two-scale model for crystal growth. (English) Zbl 1336.82015 Adv. Comput. Math. 41, No. 5, 987-1013 (2015). MSC: 82C80 65M06 65M50 80A22 82D25 80M20 PDFBibTeX XMLCite \textit{M. Redeker} and \textit{B. Haasdonk}, Adv. Comput. Math. 41, No. 5, 987--1013 (2015; Zbl 1336.82015) Full Text: DOI
Zozulya, V. V. Regularization of divergent integrals: a comparison of the classical and generalized-functions approaches. (English) Zbl 1329.65291 Adv. Comput. Math. 41, No. 4, 727-780 (2015). MSC: 65N38 35J25 65R30 PDFBibTeX XMLCite \textit{V. V. Zozulya}, Adv. Comput. Math. 41, No. 4, 727--780 (2015; Zbl 1329.65291) Full Text: DOI
Chernov, Alexey; Pham, Duong Sparse tensor product spectral Galerkin BEM for elliptic problems with random input data on a spheroid. (English) Zbl 1308.65194 Adv. Comput. Math. 41, No. 1, 77-104 (2015). MSC: 65N30 35R60 41A25 PDFBibTeX XMLCite \textit{A. Chernov} and \textit{D. Pham}, Adv. Comput. Math. 41, No. 1, 77--104 (2015; Zbl 1308.65194) Full Text: DOI
Domínguez, Víctor; Lu, Sijiang L.; Sayas, Francisco-Javier A Nyström method for the two dimensional Helmholtz hypersingular equation. (English) Zbl 1310.65153 Adv. Comput. Math. 40, No. 5-6, 1121-1157 (2014). Reviewer: Andreas Kleefeld (Cottbus) MSC: 65N38 65N12 35J05 PDFBibTeX XMLCite \textit{V. Domínguez} et al., Adv. Comput. Math. 40, No. 5--6, 1121--1157 (2014; Zbl 1310.65153) Full Text: DOI arXiv
Lechleiter, Armin; Nguyen, Dinh-Liem A trigonometric Galerkin method for volume integral equations arising in TM grating scattering. (English) Zbl 1304.78010 Adv. Comput. Math. 40, No. 1, 1-25 (2014). MSC: 78A45 65R20 65N35 65T40 65T50 78M22 PDFBibTeX XMLCite \textit{A. Lechleiter} and \textit{D.-L. Nguyen}, Adv. Comput. Math. 40, No. 1, 1--25 (2014; Zbl 1304.78010) Full Text: DOI arXiv
Melenk, J. M.; Xenophontos, C.; Oberbroeckling, L. Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales. (English) Zbl 1278.34064 Adv. Comput. Math. 39, No. 2, 367-394 (2013). Reviewer: Robert Vrabel (Trnava) MSC: 34E05 65L11 34E13 34B05 34E15 PDFBibTeX XMLCite \textit{J. M. Melenk} et al., Adv. Comput. Math. 39, No. 2, 367--394 (2013; Zbl 1278.34064) Full Text: DOI arXiv
Li, Jichun; Gonzalez, Oscar Convergence and conditioning of a Nyström method for Stokes flow in exterior three-dimensional domains. (English) Zbl 1273.76086 Adv. Comput. Math. 39, No. 1, 143-174 (2013). MSC: 76D07 65N38 76M15 PDFBibTeX XMLCite \textit{J. Li} and \textit{O. Gonzalez}, Adv. Comput. Math. 39, No. 1, 143--174 (2013; Zbl 1273.76086) Full Text: DOI
Ye, Weicai; Zhang, Yongdong A fast solver for integral equations with convolution-type kernel. (English) Zbl 1275.65096 Adv. Comput. Math. 39, No. 1, 45-67 (2013). Reviewer: Ilia V. Boikov (Penza) MSC: 65R20 45E10 65Y05 65Y20 PDFBibTeX XMLCite \textit{W. Ye} and \textit{Y. Zhang}, Adv. Comput. Math. 39, No. 1, 45--67 (2013; Zbl 1275.65096) Full Text: DOI
Hiptmair, R.; Jerez-Hanckes, C. Multiple traces boundary integral formulation for Helmholtz transmission problems. (English) Zbl 1261.65123 Adv. Comput. Math. 37, No. 1, 39-91 (2012). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65N38 65N12 35J05 PDFBibTeX XMLCite \textit{R. Hiptmair} and \textit{C. Jerez-Hanckes}, Adv. Comput. Math. 37, No. 1, 39--91 (2012; Zbl 1261.65123) Full Text: DOI Link
Brenner, Marty; Jiang, Ying; Xu, Yuesheng Multiparameter regularization for Volterra kernel identification via multiscale collocation methods. (English) Zbl 1190.65200 Adv. Comput. Math. 31, No. 4, 421-455 (2009). Reviewer: Josef Kofroň (Praha) MSC: 65R32 65R20 47A52 45D05 45Q05 65R30 PDFBibTeX XMLCite \textit{M. Brenner} et al., Adv. Comput. Math. 31, No. 4, 421--455 (2009; Zbl 1190.65200) Full Text: DOI
Liu, Yang; Hu, Qiya; Yu, Dehao A non-overlapping domain decomposition for low-frequency time-harmonic Maxwell’s equations in unbounded domains. (English) Zbl 1151.78369 Adv. Comput. Math. 28, No. 4, 355-382 (2008). MSC: 78M10 78M15 65N55 PDFBibTeX XMLCite \textit{Y. Liu} et al., Adv. Comput. Math. 28, No. 4, 355--382 (2008; Zbl 1151.78369) Full Text: DOI
Zampieri, Elena; Pavarino, Luca F. An explicit second order spectral element method for acoustic waves. (English) Zbl 1118.65106 Adv. Comput. Math. 25, No. 4, 381-401 (2006). MSC: 65M60 65M70 65M12 35L05 PDFBibTeX XMLCite \textit{E. Zampieri} and \textit{L. F. Pavarino}, Adv. Comput. Math. 25, No. 4, 381--401 (2006; Zbl 1118.65106) Full Text: DOI
Schneider, Reinhold; Xu, Yuesheng; Zhou, Aihui An analysis of discontinuous Galerkin methods for elliptic problems. (English) Zbl 1099.65116 Adv. Comput. Math. 25, No. 1-3, 259-286 (2006). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 65N30 65N15 65Y05 35J25 PDFBibTeX XMLCite \textit{R. Schneider} et al., Adv. Comput. Math. 25, No. 1--3, 259--286 (2006; Zbl 1099.65116) Full Text: DOI
Huang, Min A construction of multiscale bases for Petrov-Galerkin methods for integral equations. (English) Zbl 1098.65121 Adv. Comput. Math. 25, No. 1-3, 7-22 (2006). Reviewer: Hu Chuangan (Tianjin) MSC: 65R20 45E10 PDFBibTeX XMLCite \textit{M. Huang}, Adv. Comput. Math. 25, No. 1--3, 7--22 (2006; Zbl 1098.65121) Full Text: DOI
Hansen, Olaf A fast collocation method for the radiosity equation, based on the hierarchical algorithm of Hanrahan and Salzman: the 1D case. (English) Zbl 1072.65165 Adv. Comput. Math. 22, No. 4, 353-375 (2005). Reviewer: Nikolay Yakovlevich Tikhonenko (Odessa) MSC: 65R20 65Y20 45E10 PDFBibTeX XMLCite \textit{O. Hansen}, Adv. Comput. Math. 22, No. 4, 353--375 (2005; Zbl 1072.65165) Full Text: DOI
Sun, Jiachang; Li, Huiyuan Generalized Fourier transform on an arbitrary triangular domain. (English) Zbl 1061.42021 Adv. Comput. Math. 22, No. 3, 223-248 (2005). Reviewer: Manfred Tasche (Rostock) MSC: 42C15 42C30 PDFBibTeX XMLCite \textit{J. Sun} and \textit{H. Li}, Adv. Comput. Math. 22, No. 3, 223--248 (2005; Zbl 1061.42021) Full Text: DOI
Khoromskij, Boris N.; Prößdorf, Siegfried Fast compuations with the harmonic Poincaré-Steklov operators on nested refined meshes. (English) Zbl 0895.65047 Adv. Comput. Math. 8, No. 1-2, 111-135 (1998). Reviewer: A.Handlovičová (Bratislava) MSC: 65N30 65N50 35J25 PDFBibTeX XMLCite \textit{B. N. Khoromskij} and \textit{S. Prößdorf}, Adv. Comput. Math. 8, No. 1--2, 111--135 (1998; Zbl 0895.65047) Full Text: DOI
Khoromskij, Boris N.; Prößdorf, Siegfried Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation. (English) Zbl 0839.65129 Adv. Comput. Math. 4, No. 4, 331-355 (1995). Reviewer: H.P.Dikshit (Jabalpur) MSC: 65N38 65F35 35J05 PDFBibTeX XMLCite \textit{B. N. Khoromskij} and \textit{S. Prößdorf}, Adv. Comput. Math. 4, No. 4, 331--355 (1995; Zbl 0839.65129) Full Text: DOI