Wessels, Henning; Weißenfels, Christian; Wriggers, Peter The neural particle method - an updated Lagrangian physics informed neural network for computational fluid dynamics. (English) Zbl 1506.76136 Comput. Methods Appl. Mech. Eng. 368, Article ID 113127, 15 p. (2020). MSC: 76M28 76Bxx PDFBibTeX XMLCite \textit{H. Wessels} et al., Comput. Methods Appl. Mech. Eng. 368, Article ID 113127, 15 p. (2020; Zbl 1506.76136) Full Text: DOI arXiv
Araya, Rodolfo; Harder, Christopher; Poza, Abner H.; Valentin, Frédéric Multiscale hybrid-mixed method for the Stokes and Brinkman equations – the method. (English) Zbl 1439.76046 Comput. Methods Appl. Mech. Eng. 324, 29-53 (2017). MSC: 76M10 65N30 65N12 76D07 76S05 PDFBibTeX XMLCite \textit{R. Araya} et al., Comput. Methods Appl. Mech. Eng. 324, 29--53 (2017; Zbl 1439.76046) Full Text: DOI
Marras, Simone; Kelly, James F.; Moragues, Margarida; Müller, Andreas; Kopera, Michal A.; Vázquez, Mariano; Giraldo, Francis X.; Houzeaux, Guillaume; Jorba, Oriol A review of element-based Galerkin methods for numerical weather prediction: finite elements, spectral elements, and discontinuous Galerkin. (English) Zbl 1360.86004 Arch. Comput. Methods Eng. 23, No. 4, 673-722 (2016). MSC: 86-08 86A10 76M10 65M60 PDFBibTeX XMLCite \textit{S. Marras} et al., Arch. Comput. Methods Eng. 23, No. 4, 673--722 (2016; Zbl 1360.86004) Full Text: DOI Link
Marras, Simone; Moragues, Margarida; Vázquez, Mariano; Jorba, Oriol; Houzeaux, Guillaume Simulations of moist convection by a variational multiscale stabilized finite element method. (English) Zbl 1349.86037 J. Comput. Phys. 252, 195-218 (2013). MSC: 86A10 65M08 PDFBibTeX XMLCite \textit{S. Marras} et al., J. Comput. Phys. 252, 195--218 (2013; Zbl 1349.86037) Full Text: DOI
Marras, Simone; Moragues, Margarida; Vázquez, Mariano; Jorba, Oriol; Houzeaux, Guillaume A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows. (English) Zbl 1286.65126 J. Comput. Phys. 236, 380-407 (2013). MSC: 65M60 76M10 65M12 35Q31 PDFBibTeX XMLCite \textit{S. Marras} et al., J. Comput. Phys. 236, 380--407 (2013; Zbl 1286.65126) Full Text: DOI
Allendes, Alejandro; Barrenechea, Gabriel R.; Hernández, Erwin; Valentin, Frédéric A two-level enriched finite element method for a mixed problem. (English) Zbl 1220.65162 Math. Comput. 80, No. 273, 11-41 (2011). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N30 65N12 76S05 76M10 35Q35 PDFBibTeX XMLCite \textit{A. Allendes} et al., Math. Comput. 80, No. 273, 11--41 (2011; Zbl 1220.65162) Full Text: DOI
Hachem, E.; Rivaux, B.; Kloczko, Thibaud; Digonnet, Hugues; Coupez, Thierry Stabilized finite element method for incompressible flows with high Reynolds number. (English) Zbl 1282.76120 J. Comput. Phys. 229, No. 23, 8643-8665 (2010). MSC: 76M10 PDFBibTeX XMLCite \textit{E. Hachem} et al., J. Comput. Phys. 229, No. 23, 8643--8665 (2010; Zbl 1282.76120) Full Text: DOI
Nesliturk, A. I.; Aydın, S. H.; Tezer-Sezgin, M. Two-level finite element method with a stabilizing subgrid for the incompressible Navier-Stokes equations. (English) Zbl 1145.76032 Int. J. Numer. Methods Fluids 58, No. 5, 551-572 (2008). MSC: 76M10 76D05 PDFBibTeX XMLCite \textit{A. I. Nesliturk} et al., Int. J. Numer. Methods Fluids 58, No. 5, 551--572 (2008; Zbl 1145.76032) Full Text: DOI Link
Gravemeier, V. The variational multiscale method for laminar and turbulent flow. (English) Zbl 1177.76341 Arch. Comput. Methods Eng. 13, No. 2, 249-324 (2006). MSC: 76M30 76F65 76M45 76M25 65M06 76-02 PDFBibTeX XMLCite \textit{V. Gravemeier}, Arch. Comput. Methods Eng. 13, No. 2, 249--324 (2006; Zbl 1177.76341) Full Text: DOI
Cangiani, Andrea; Süli, Endre Enhanced RFB method. (English) Zbl 1085.65108 Numer. Math. 101, No. 2, 273-308 (2005). Reviewer: Myron Sussman (Bethel Park) MSC: 65N30 35J25 65N15 65N50 PDFBibTeX XMLCite \textit{A. Cangiani} and \textit{E. Süli}, Numer. Math. 101, No. 2, 273--308 (2005; Zbl 1085.65108) Full Text: DOI
Gravemeier, Volker; Wall, Wolfgang A.; Ramm, Ekkehard A three-level finite element method for the instationary incompressible Navier-Stokes equations. (English) Zbl 1085.76038 Comput. Methods Appl. Mech. Eng. 193, No. 15-16, 1323-1366 (2004). MSC: 76M10 76D05 PDFBibTeX XMLCite \textit{V. Gravemeier} et al., Comput. Methods Appl. Mech. Eng. 193, No. 15--16, 1323--1366 (2004; Zbl 1085.76038) Full Text: DOI
Ye, Xiu; Xu, Chaoyong A discontinuous Galerkin method for the Reissner-Mindlin plate in the primitive variables. (English) Zbl 1044.74045 Appl. Math. Comput. 149, No. 1, 65-82 (2004). MSC: 74S05 74K20 PDFBibTeX XMLCite \textit{X. Ye} and \textit{C. Xu}, Appl. Math. Comput. 149, No. 1, 65--82 (2004; Zbl 1044.74045) Full Text: DOI
Maniatty, Antoinette M.; Liu, Yong Stabilized finite element method for viscoplastic flow: formulation with state variable evolution. (English) Zbl 1116.74431 Int. J. Numer. Methods Eng. 56, No. 2, 185-209 (2003). MSC: 74S05 74C10 PDFBibTeX XMLCite \textit{A. M. Maniatty} and \textit{Y. Liu}, Int. J. Numer. Methods Eng. 56, No. 2, 185--209 (2003; Zbl 1116.74431) Full Text: DOI
Engel, G.; Garikipati, K.; Hughes, T. J. R.; Larson, M. G.; Mazzei, L.; Taylor, R. L. Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. (English) Zbl 1086.74038 Comput. Methods Appl. Mech. Eng. 191, No. 34, 3669-3750 (2002). MSC: 74S05 74K10 74K20 74B99 PDFBibTeX XMLCite \textit{G. Engel} et al., Comput. Methods Appl. Mech. Eng. 191, No. 34, 3669--3750 (2002; Zbl 1086.74038) Full Text: DOI
Fischer, B.; Ramage, A.; Silvester, D. J.; Wathen, A. J. On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems. (English) Zbl 0977.76043 Comput. Methods Appl. Mech. Eng. 179, No. 1-2, 179-195 (1999). MSC: 76M10 76R99 PDFBibTeX XMLCite \textit{B. Fischer} et al., Comput. Methods Appl. Mech. Eng. 179, No. 1--2, 179--195 (1999; Zbl 0977.76043) Full Text: DOI
Blank, Henrik; Rudgyard, Michael; Wathen, Andrew Stabilised finite element methods for steady incompressible flow. (English) Zbl 0957.76025 Comput. Methods Appl. Mech. Eng. 174, No. 1-2, 91-105 (1999). MSC: 76M10 76D05 76R99 PDFBibTeX XMLCite \textit{H. Blank} et al., Comput. Methods Appl. Mech. Eng. 174, No. 1--2, 91--105 (1999; Zbl 0957.76025) Full Text: DOI
Li, Jichun; Navon, I. M. Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type. (English) Zbl 0936.65134 Comput. Methods Appl. Mech. Eng. 162, No. 1-4, 49-78 (1998). MSC: 65N30 65N12 35B25 35J25 PDFBibTeX XMLCite \textit{J. Li} and \textit{I. M. Navon}, Comput. Methods Appl. Mech. Eng. 162, No. 1--4, 49--78 (1998; Zbl 0936.65134) Full Text: DOI
Bertoluzza, S. Stabilization by multiscale decomposition. (English) Zbl 0940.65060 Appl. Math. Lett. 11, No. 6, 129-134 (1998). MSC: 65J10 35J25 47A50 65N30 65N12 PDFBibTeX XMLCite \textit{S. Bertoluzza}, Appl. Math. Lett. 11, No. 6, 129--134 (1998; Zbl 0940.65060) Full Text: DOI
Norburn, Sean; Silvester, David Stabilised vs. stable mixed methods for incompressible flow. (English) Zbl 0940.76036 Comput. Methods Appl. Mech. Eng. 166, No. 1-2, 131-141 (1998). MSC: 76M10 76D05 65N12 PDFBibTeX XMLCite \textit{S. Norburn} and \textit{D. Silvester}, Comput. Methods Appl. Mech. Eng. 166, No. 1--2, 131--141 (1998; Zbl 0940.76036) Full Text: DOI
Rannacher, Rolf A posteriori error estimation in least-squares stabilized finite element schemes. (English) Zbl 0934.65118 Comput. Methods Appl. Mech. Eng. 166, No. 1-2, 99-114 (1998). Reviewer: Myron Sussman (Bethel Park) MSC: 65N15 76M10 76D07 35Q30 65N30 65N50 35J05 PDFBibTeX XMLCite \textit{R. Rannacher}, Comput. Methods Appl. Mech. Eng. 166, No. 1--2, 99--114 (1998; Zbl 0934.65118) Full Text: DOI