Jang, Yongseok; Bonelle, Jérôme; Kruse, Carola; Hülsemann, Frank; Rüde, Ulrich Fast linear solvers for incompressible CFD simulations with compatible discrete operator schemes. (English) Zbl 07978669 Comput. Appl. Math. 44, No. 1, Paper No. 79, 36 p. (2025). MSC: 65F08 65F10 65M22 76D05 × Cite Format Result Cite Review PDF Full Text: DOI
Ainsworth, Mark; Parker, Charles Statically condensed iterated penalty method for high order finite element discretizations of incompressible flow. (English) Zbl 1543.76074 SIAM J. Sci. Comput. 45, No. 6, A3095-A3120 (2023). MSC: 76M10 76D07 65N30 65N12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bui, Giao; López-García, Fernando; Tran, Van An application of the weighted discrete Hardy inequality. (English) Zbl 1505.26034 Math. Inequal. Appl. 25, No. 3, 771-788 (2022). MSC: 26D15 46E35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ben-Artzi, Matania; Croisille, Jean-Pierre; Fishelov, Dalia Time evolution of discrete fourth-order elliptic operators. (English) Zbl 1418.65096 Numer. Methods Partial Differ. Equations 35, No. 4, 1429-1457 (2019). MSC: 65M06 35K52 35J30 65M12 35Q35 76D05 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Malhotra, Dhairya; Biros, George Algorithm 967: A distributed-memory fast multipole method for volume potentials. (English) Zbl 1371.65125 ACM Trans. Math. Softw. 43, No. 2, Article No. 17, 27 p. (2016). MSC: 65N38 65Y05 65N80 35J05 35Q30 70F10 65N75 × Cite Format Result Cite Review PDF Full Text: DOI
Han, Houde; Wu, Xiaonan A survey on artificial boundary method. (English) Zbl 1304.35490 Sci. China, Math. 56, No. 12, 2439-2488 (2013). MSC: 35Q30 65M06 65M12 65M85 65N06 65N12 65N85 35J47 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Fu, Huankun; Liu, Chaoqun A buffered Fourier spectral method for non-periodic PDE. (English) Zbl 1279.65120 Int. J. Numer. Anal. Model. 9, No. 2, 460-478 (2012). MSC: 65M70 65N35 35Q30 65T50 35J05 × Cite Format Result Cite Review PDF Full Text: Link
Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. A review of unified a posteriori finite element error control. (English) Zbl 1289.65249 Numer. Math., Theory Methods Appl. 5, No. 4, 509-558 (2012). MSC: 65N15 65N30 35J05 65M20 35Q30 65M15 65M60 × Cite Format Result Cite Review PDF Full Text: DOI Link
Chen, Kevin K.; Tu, Jonathan H.; Rowley, Clarence W. Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses. (English) Zbl 1259.35009 J. Nonlinear Sci. 22, No. 6, 887-915 (2012). MSC: 35A25 35G61 35P15 37M10 37N10 35A35 35Q30 × Cite Format Result Cite Review PDF Full Text: DOI
Paycha, Sylvie Regularised integrals, sums and traces. An analytic point of view. (English) Zbl 1272.11103 University Lecture Series 59. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5367-2/pbk). x, 190 p. (2012). Reviewer: Emilio Elizalde (Bellaterra) MSC: 11M36 11-02 47-02 11M06 35R01 35S05 47G30 58J40 47L80 × Cite Format Result Cite Review PDF
Mardal, Kent-Andre; Winther, Ragnar Preconditioning discretizations of systems of partial differential equations. (English) Zbl 1249.65246 Numer. Linear Algebra Appl. 18, No. 1, 1-40 (2011). Reviewer: Tomáš Vejchodský (Praha) MSC: 65N30 65F08 35J05 35Q30 35Q61 35K57 74K20 65K10 49J15 35B25 65F10 × Cite Format Result Cite Review PDF Full Text: DOI
Hidalgo, Rubén A.; Godoy Molina, Mauricio Navier-Stokes equations on weighted graphs. (English) Zbl 1221.05114 Complex Anal. Oper. Theory 4, No. 3, 525-540 (2010). MSC: 05C12 39A12 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Oseledets, Ivan; Muravleva, Ekaterina Fast orthogonalization to the kernel of the discrete gradient operator with application to Stokes problem. (English) Zbl 1183.65131 Linear Algebra Appl. 432, No. 6, 1492-1500 (2010). MSC: 65N06 35J25 35Q30 × Cite Format Result Cite Review PDF Full Text: DOI
Pokotilo, V. I. Semiclassical approximation for the non-self-adjoint Sturm-Liouville problem with the potential \(q(x) = x^{4} - a^{2}x^{2}\). (English. Russian original) Zbl 1181.34093 Math. Notes 85, No. 5, 755-759 (2009); translation from Mat. Zametki 85, No. 5, 792-796 (2009). MSC: 34L15 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Bochev, Pavel B.; Gunzburger, Max D. Least-squares finite element methods. (English) Zbl 1168.65067 Applied Mathematical Sciences 166. New York, NY: Springer (ISBN 978-0-387-30888-3/hbk; 978-0-387-68922-7/ebook). xxii, 660 p. (2009). Reviewer: Dietrich Braess (Bochum) MSC: 65N30 35Q60 35K15 35L15 65M55 65N55 65M60 35J05 46E35 35Q30 × Cite Format Result Cite Review PDF Full Text: DOI
Kikuchi, Norio; Nakai, Eiichi; Tomita, Naohito; Yabuta, Kôzô; Yoneda, Tsuyoshi Calderón-Zygmund operators on amalgam spaces and in the discrete case. (English) Zbl 1125.43001 J. Math. Anal. Appl. 335, No. 1, 198-212 (2007). Reviewer: Michael J. Puls (New York) MSC: 43A15 47B37 × Cite Format Result Cite Review PDF Full Text: DOI
Bochev, Pavel B.; Gunzburger, Max D.; Lehoucq, Richard B. On stabilized finite element methods for the Stokes problem in the small time step limit. (English) Zbl 1104.76059 Int. J. Numer. Methods Fluids 53, No. 4, 573-597 (2007). MSC: 76M10 76D07 × Cite Format Result Cite Review PDF Full Text: DOI Link
Blair Perot, J.; Vidovic, Dragan; Wesseling, Pieter Mimetic reconstruction of vectors. (English) Zbl 1110.65108 Arnold, Douglas N. (ed.) et al., Compatible spatial discretizations. Papers presented at IMA hot topics workshop: compatible spatial discretizations for partial differential equations, Minneapolis, MN, USA, May 11–15, 2004. New York, NY: Springer (ISBN 0-387-30916-0/hbk). The IMA Volumes in Mathematics and its Applications 142, 173-188 (2006). MSC: 65N30 65M60 76M10 35J05 35Q30 76M12 35Q60 × Cite Format Result Cite Review PDF
Ying, Lexing; Biros, George; Zorin, Denis A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. (English) Zbl 1105.65115 J. Comput. Phys. 219, No. 1, 247-275 (2006). MSC: 65N38 35J25 35J05 35Q30 65T50 × Cite Format Result Cite Review PDF Full Text: DOI
Junk, Michael; Klar, Axel; Luo, Li-Shi Asymptotic analysis of the lattice Boltzmann equation. (English) Zbl 1079.82013 J. Comput. Phys. 210, No. 2, 676-704 (2005). Reviewer: Iván Abonyi (Budapest) MSC: 82C40 76D05 76P05 76M45 × Cite Format Result Cite Review PDF Full Text: DOI
Avital, E. J. A second look at the role of the fast Fourier transform as an elliptic solver. (English) Zbl 1073.65110 Int. J. Numer. Methods Fluids 48, No. 9, 909-927 (2005). MSC: 65N06 65T50 35J05 35Q30 76D05 76M20 × Cite Format Result Cite Review PDF Full Text: DOI
Wathen, A.; Loghin, D.; Kay, D.; Elman, H.; Silvester, D. A new preconditioner for the Oseen equations. (English) Zbl 1268.76036 Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer (ISBN 88-470-0180-3/hbk). 979-988 (2003). MSC: 76M10 76D07 × Cite Format Result Cite Review PDF
Pflaum, Christoph Expression templates for partial differential equations. (English) Zbl 0996.65117 Comput. Vis. Sci. 4, No. 1, 1-8 (2001). MSC: 65N30 35-04 65Y15 35Q30 35J05 35J65 × Cite Format Result Cite Review PDF Full Text: DOI
Hill, Adrian T.; Süli, Endre Approximation of the global attractor for the incompressible Navier-Stokes equations. (English) Zbl 0982.76022 IMA J. Numer. Anal. 20, No. 4, 633-667 (2000). MSC: 76D05 76M10 35Q30 × Cite Format Result Cite Review PDF Full Text: DOI
Pavlov, A. N.; Sazhin, S. S.; Fedorenko, R. P.; Heikal, M. R. A conservative finite difference method and its application for the analysis of a transient flow around a square prism. (English) Zbl 0966.76061 Int. J. Numer. Methods Heat Fluid Flow 10, No. 1, 6-46 (2000). MSC: 76M20 76D25 76D05 × Cite Format Result Cite Review PDF Full Text: DOI
Harrison, J. Flux across nonsmooth boundaries and fractal Gauss/Green/Stokes’ theorems. (English) Zbl 0944.39006 J. Phys. A, Math. Gen. 32, No. 28, 5317-5327 (1999). Reviewer: Th.M.Rassias (Athens) MSC: 39A12 49Q20 26B20 × Cite Format Result Cite Review PDF Full Text: DOI
Fischer, Paul F. Projection techniques for iterative solution of \(A\underline x=\underline b\) with successive right-hand sides. (English) Zbl 0960.76063 Comput. Methods Appl. Mech. Eng. 163, No. 1-4, 193-204 (1998). MSC: 76M22 76D05 65F10 × Cite Format Result Cite Review PDF Full Text: DOI
Canuto, Claudio; Russo, Alessandro; van Kemenade, Vincent Stabilized spectral methods for the Navier-Stokes equations: residual-free bubbles and preconditioning. (English) Zbl 0940.76058 Comput. Methods Appl. Mech. Eng. 166, No. 1-2, 65-83 (1998). MSC: 76M22 76D05 × Cite Format Result Cite Review PDF Full Text: DOI
Koiller, J.; Raupp, M. A.; Delgado, J.; Ehlers, K. M.; Montgomery, R. Spectral methods for Stokes flows. (English) Zbl 0916.76053 Comput. Appl. Math. 17, No. 3, 343-371 (1998). MSC: 76M25 76D07 35Q30 × Cite Format Result Cite Review PDF
Wetton, Brian R. Analysis of the spatial error for a class of finite difference methods for viscous incompressible flow. (English) Zbl 0886.76061 SIAM J. Numer. Anal. 34, No. 2, 723-755 (1997). Reviewer: A.Meister (Hamburg) MSC: 76M20 76D05 65M06 × Cite Format Result Cite Review PDF Full Text: DOI
Algazin, S. D. Numerical study of the Stokes equations. (English. Russian original) Zbl 0999.76572 Prikl. Mekh. Tekh. Fiz. 36, No. 5, 48-56 (1995); translation in J. Appl. Mech. Tech. Phys. 36, No. 5, 682-688 (1995). Reviewer: V.I.Pinchukov (Novosibirsk) MSC: 76M20 76D05 × Cite Format Result Cite Review PDF
Tau, Eric Yu A second-order projection method for the incompressible Navier-Stokes equations in arbitrary domains. (English) Zbl 0811.76064 J. Comput. Phys. 115, No. 1, 147-152 (1994). MSC: 76M25 76M20 76D05 × Cite Format Result Cite Review PDF Full Text: DOI
Souli, M. A variational finite element method for the two-dimensional Stokes problem. (English) Zbl 0845.76050 Comput. Methods Appl. Mech. Eng. 108, No. 3-4, 223-236 (1993). MSC: 76M10 76M30 76D07 × Cite Format Result Cite Review PDF Full Text: DOI
Wathen, Andrew; Silvester, David Fast iterative solution of stabilised Stokes systems. I: Using simple diagonal preconditions. (English) Zbl 0776.76024 SIAM J. Numer. Anal. 30, No. 3, 630-649 (1993). MSC: 76D07 76M10 65N30 65F10 × Cite Format Result Cite Review PDF Full Text: DOI
Iooss, G.; Mielke, A. Reduction and normalization of hydrodynamical stability problems in infinitely long cylinders. (English) Zbl 0777.76040 Trends in applications of mathematics to mechanics, Proc. 8th Symp., STAMM-8, Hollabrunn/Austria 1989, 43-56 (1991). Reviewer: A.Georgescu (Bucureşti) MSC: 76E99 35B32 37A30 × Cite Format Result Cite Review PDF
Gürlebeck, Klaus Grundlagen einer diskreten räumlich verallgemeinerten Funktionentheorie und ihrer Anwendungen. (Foundations of a discrete spatially generalised function theory and its applications). (German) Zbl 0704.35043 Karl-Marx-Stadt: Techn. Univ. Karl-Marx-Stadt, Fak. für Mathematik und Naturwissenschaften, Diss. iii, 122 S. (1988). MSC: 35J55 32A45 35Q30 × Cite Format Result Cite Review PDF
Hughes, Thomas J. R.; Mallet, Michel A new finite element formulation for computational fluid dynamics. IV: A discontinuity-capturing operator for multidimensional advective-diffusive systems. (English) Zbl 0587.76120 Comput. Methods Appl. Mech. Eng. 58, 329-336 (1986). MSC: 76N10 65Z05 76N15 76R99 80A20 × Cite Format Result Cite Review PDF Full Text: DOI
Hall, C. A.; Peterson, J. S.; Porsching, T. A.; Sledge, F. R. The dual variable method for finite element discretizations of Navier/Stokes equations. (English) Zbl 0587.76045 Int. J. Numer. Methods Eng. 21, 883-898 (1985). MSC: 76D05 76D10 76M99 65N06 35Q30 × Cite Format Result Cite Review PDF Full Text: DOI
Park, K. C. Locking, spurious mechanisms, and pressure divergence in penalty finite element methods for Stokes flow problems. (English) Zbl 0545.76040 Comput. Methods Appl. Mech. Eng. 47, 315-330 (1984). MSC: 76D07 76M99 × Cite Format Result Cite Review PDF Full Text: DOI
Park, K. C. Locking, spurious mechanisms, and pressure divergence in penalty finite element methods for Stokes flow problems. (English) Zbl 0534.76043 Comput. Methods Appl. Mech. Eng. (to appear). MSC: 76D07 76M99 × Cite Format Result Cite Review PDF
Malkus, D. S. Incompressible finite elements: The LBB condition and the discrete eigenstructure. (English) Zbl 0472.73088 Nonlinear finite element analysis in structural mechanics, Proc. Europe- U.S. Workshop, Bochum 1980, 696-711 (1981). MSC: 74S05 49M29 49S05 49M30 × Cite Format Result Cite Review PDF
Malkus, D. S. Eigenproblems associated with the discrete LBB condition for incompressible finite elements. (English) Zbl 0457.73051 Int. J. Eng. Sci. 19, 1299-1310 (1981). Reviewer: H. Bufler MSC: 74S05 65N25 49M29 49S05 × Cite Format Result Cite Review PDF Full Text: DOI