Patel, Dhruv; Ray, Deep; Abdelmalik, Michael R. A.; Hughes, Thomas J. R.; Oberai, Assad A. Variationally mimetic operator networks. (English) Zbl 07796642 Comput. Methods Appl. Mech. Eng. 419, Article ID 116536, 30 p. (2024). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{D. Patel} et al., Comput. Methods Appl. Mech. Eng. 419, Article ID 116536, 30 p. (2024; Zbl 07796642) Full Text: DOI arXiv
Pousin, Jerome Some elliptic second order problems and neural network solutions: existence and error estimates. (English) Zbl 1522.65245 J. Comput. Appl. Math. 436, Article ID 115398, 13 p. (2024). MSC: 65N99 68T07 PDFBibTeX XMLCite \textit{J. Pousin}, J. Comput. Appl. Math. 436, Article ID 115398, 13 p. (2024; Zbl 1522.65245) Full Text: DOI
Guerder, Marie; Duval, Arnaud; Elguedj, Thomas; Dam, Damien Volumetric embedded entities for the isogeometric analysis of complex structures. (English) Zbl 07788110 Comput. Methods Appl. Mech. Eng. 417, Part B, Article ID 116426, 29 p. (2023). MSC: 74-XX 68-XX PDFBibTeX XMLCite \textit{M. Guerder} et al., Comput. Methods Appl. Mech. Eng. 417, Part B, Article ID 116426, 29 p. (2023; Zbl 07788110) Full Text: DOI
Aznaran, Francis R. A.; Farrell, Patrick E.; Kirby, Robert C. Transformations for Piola-mapped elements. (English) Zbl 1528.65099 SMAI J. Comput. Math. 8, 399-437 (2023). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N55 65F08 65F10 76D07 74B10 35A15 68W30 78M10 PDFBibTeX XMLCite \textit{F. R. A. Aznaran} et al., SMAI J. Comput. Math. 8, 399--437 (2023; Zbl 1528.65099) Full Text: DOI arXiv
Innerberger, Michael; Praetorius, Dirk MooAFEM: an object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs. (English) Zbl 1511.65003 Appl. Math. Comput. 442, Article ID 127731, 17 p. (2023). MSC: 65-04 65N30 65N50 68W30 PDFBibTeX XMLCite \textit{M. Innerberger} and \textit{D. Praetorius}, Appl. Math. Comput. 442, Article ID 127731, 17 p. (2023; Zbl 1511.65003) Full Text: DOI arXiv
Balu, Aditya; Rajanna, Manoj R.; Khristy, Joel; Xu, Fei; Krishnamurthy, Adarsh; Hsu, Ming-Chen Direct immersogeometric fluid flow and heat transfer analysis of objects represented by point clouds. (English) Zbl 07644832 Comput. Methods Appl. Mech. Eng. 404, Article ID 115742, 34 p. (2023). MSC: 76-XX 68-XX PDFBibTeX XMLCite \textit{A. Balu} et al., Comput. Methods Appl. Mech. Eng. 404, Article ID 115742, 34 p. (2023; Zbl 07644832) Full Text: DOI arXiv
Georgoulis, Emmanuil H.; Loulakis, Michail; Tsiourvas, Asterios Discrete gradient flow approximations of high dimensional evolution partial differential equations via deep neural networks. (English) Zbl 07634536 Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106893, 11 p. (2023). MSC: 68Txx 65Mxx 65Cxx PDFBibTeX XMLCite \textit{E. H. Georgoulis} et al., Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106893, 11 p. (2023; Zbl 07634536) Full Text: DOI arXiv
Berrone, Stefano; Canuto, Claudio; Pintore, Moreno Variational physics informed neural networks: the role of quadratures and test functions. (English) Zbl 07568992 J. Sci. Comput. 92, No. 3, Paper No. 100, 27 p. (2022). MSC: 65-XX 35B45 35J20 35Q93 65K10 65N20 68T07 PDFBibTeX XMLCite \textit{S. Berrone} et al., J. Sci. Comput. 92, No. 3, Paper No. 100, 27 p. (2022; Zbl 07568992) Full Text: DOI arXiv
Cagnetti, Filippo; Chambolle, Antonin; Scardia, Lucia Korn and Poincaré-Korn inequalities for functions with a small jump set. (English) Zbl 07566700 Math. Ann. 383, No. 3-4, 1179-1216 (2022). MSC: 68-XX 35-XX PDFBibTeX XMLCite \textit{F. Cagnetti} et al., Math. Ann. 383, No. 3--4, 1179--1216 (2022; Zbl 07566700) Full Text: DOI
Huang, Jianguo; Wang, Haoqin; Zhou, Tao An augmented Lagrangian deep learning method for variational problems with essential boundary conditions. (English) Zbl 1482.65226 Commun. Comput. Phys. 31, No. 3, 966-986 (2022). MSC: 65N99 65N25 65N30 68T07 PDFBibTeX XMLCite \textit{J. Huang} et al., Commun. Comput. Phys. 31, No. 3, 966--986 (2022; Zbl 1482.65226) Full Text: DOI arXiv
Dokken, Jørgen S.; Funke, Simon W.; Johansson, August; Schmidt, Stephan Shape optimization using the finite element method on multiple meshes with Nitsche coupling. (English) Zbl 1432.35211 SIAM J. Sci. Comput. 41, No. 3, A1923-A1948 (2019). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35Q93 49Q10 65M85 65N30 68N99 76B75 PDFBibTeX XMLCite \textit{J. S. Dokken} et al., SIAM J. Sci. Comput. 41, No. 3, A1923--A1948 (2019; Zbl 1432.35211) Full Text: DOI
Fehr, Jörg; Heiland, Jan; Himpe, Christian; Saak, Jens Best practices for replicability, reproducibility and reusability of computer-based experiments exemplified by model reduction software. (English) Zbl 07129995 AIMS Math. 1, No. 3, 261-281 (2016). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{J. Fehr} et al., AIMS Math. 1, No. 3, 261--281 (2016; Zbl 07129995) Full Text: DOI arXiv
Guo, Yujie; Ruess, Martin Weak Dirichlet boundary conditions for trimmed thin isogeometric shells. (English) Zbl 1443.65331 Comput. Math. Appl. 70, No. 7, 1425-1440 (2015). MSC: 65N30 65D17 68U07 74K25 PDFBibTeX XMLCite \textit{Y. Guo} and \textit{M. Ruess}, Comput. Math. Appl. 70, No. 7, 1425--1440 (2015; Zbl 1443.65331) Full Text: DOI
Klinger, Matthias A variational approach for physically based image interpolation across boundaries. (English) Zbl 1382.94019 Carraro, Thomas (ed.) et al., Multiple shooting and time domain decomposition methods. MuS-TDD, Heidelberg, Germany, May 6–8, 2013. Cham: Springer (ISBN 978-3-319-23320-8/hbk; 978-3-319-23321-5/ebook). Contributions in Mathematical and Computational Sciences 9, 315-354 (2015). MSC: 94A08 49N45 49M15 65M60 68U10 76D55 76D05 PDFBibTeX XMLCite \textit{M. Klinger}, Contrib. Math. Comput. Sci. 9, 315--354 (2015; Zbl 1382.94019) Full Text: DOI
Mohan, P. Surya; Soloviev, Vadim Y.; Arridge, Simon R. Discontinuous Galerkin method for the forward modelling in optical diffusion tomography. (English) Zbl 1217.92063 Int. J. Numer. Methods Eng. 85, No. 5, 562-574 (2011). MSC: 92C55 92-08 68U10 PDFBibTeX XMLCite \textit{P. S. Mohan} et al., Int. J. Numer. Methods Eng. 85, No. 5, 562--574 (2011; Zbl 1217.92063) Full Text: DOI