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65M12 Stability and convergence of numerical methods (57 articles)

• Han, Wonho; Kim, Kwangil; Hong, Unhyok: Convergence of a proposed adaptive WENO scheme for Hamilton-Jacobi equations. (English). Applications of Mathematics, vol. 68 (2023), issue 5, pp. 661-684
• Feireisl, Eduard; Petcu, Mădălina; She, Bangwei: An entropy stable finite volume method for a compressible two phase model. (English). Applications of Mathematics, vol. 68 (2023), issue 4, pp. 467-483
• Beilina, Larisa; Ruas, Vitoriano: On the Maxwell-wave equation coupling problem and its explicit finite-element solution. (English). Applications of Mathematics, vol. 68 (2023), issue 1, pp. 75-98
• Deckelnick, Klaus; Nürnberg, Robert: An unconditionally stable finite element scheme for anisotropic curve shortening flow. (English). Archivum Mathematicum, vol. 59 (2023), issue 3, pp. 263-274
• Bastl, Bohumír; Brandner, Marek; Slabá, Kristýna; Turnerová, Eva: Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis. (English). Applications of Mathematics, vol. 67 (2022), issue 6, pp. 805-829
• Kim, Kwangil; Hong, Unhyok; Ri, Kwanhung; Yu, Juhyon: Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes. (English). Applications of Mathematics, vol. 66 (2021), issue 4, pp. 599-617
• Luo, Yuesheng; Xing, Ruixue; Li, Xiaole: A new energy conservative scheme for regularized long wave equation. (English). Applications of Mathematics, vol. 66 (2021), issue 5, pp. 745-765
• Kučera, Václav; Lukáčová-Medviďová, Mária; Noelle, Sebastian; Schütz, Jochen: Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 21-26, 2020. Institute of Mathematics CAS, Prague, 2021. pp. 69-78
• Badenjki, Abdulatif; Warnecke, Gerald: Theoretical and numerical studies of the $P_NP_M$ DG schemes in one space dimension. (English). Applications of Mathematics, vol. 64 (2019), issue 6, pp. 599-635
• Jana, Ajoy; Nair, M. Thamban: Truncated spectral regularization for an ill-posed non-linear parabolic problem. (English). Czechoslovak Mathematical Journal, vol. 69 (2019), issue 2, pp. 545-569
• Imoto, Yusuke: Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms. (English). Applications of Mathematics, vol. 64 (2019), issue 1, pp. 33-43
• Klesa, Jan: Numerical stability of the intrinsic equations for beams in time domain. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 24-29, 2018. Institute of Mathematics CAS, Prague, 2019. pp. 71-80
• Brandner, Marek; Knobloch, Petr: Some remarks concerning stabilization techniques for convection--diffusion problems. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 24-29, 2018. Institute of Mathematics CAS, Prague, 2019. pp. 35-46
• Szekeres, Béla J.; Izsák, Ferenc: Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems. (English). Applications of Mathematics, vol. 62 (2017), issue 1, pp. 15-36
• Molati, Motlatsi; Murakawa, Hideki: An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 305-314
• Stašová, Olga; Mikula, Karol; Handlovičová, Angela; Peyriéras, Nadine: Nonlinear Tensor Diffusion in Image Processing. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 377-386
• Eymard, Robert; Handlovičová, Angela; Herbin, Raphaèle; Mikula, Karol; Stašová, Olga: Applications of approximate gradient schemes for nonlinear parabolic equations. (English). Applications of Mathematics, vol. 60 (2015), issue 2, pp. 135-156
• Balázsová, Monika; Feistauer, Miloslav; Hadrava, Martin; Kosík, Adam: Stability analysis of the space-time discontinuous Galerkin method for nonstationary nonlinear convection-diffusion problems. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 9-16
• Zlatev, Zahari; Dimov, Ivan; Faragó, István; Georgiev, Krassimir; Havasi, Ágnes; Ostromsky, Tzvetan: Application of Richardson extrapolation with the Crank-Nicolson scheme for multi-dimensional advection. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 248-256
• Handlovičová, Angela; Kotorová, Dana: Numerical analysis of a semi-implicit DDFV scheme for the regularized curvature driven level set equation in 2D. (English). Kybernetika, vol. 49 (2013), issue 6, pp. 829-854
• Leszczyński, Henryk; Zwierkowski, Piotr: The Rothe method for the McKendrick-von Foerster equation. (English). Czechoslovak Mathematical Journal, vol. 63 (2013), issue 3, pp. 589-602
• Su, Haiyan; Huang, Pengzhan; Feng, Xinlong: Two-level stabilized nonconforming finite element method for the Stokes equations. (English). Applications of Mathematics, vol. 58 (2013), issue 6, pp. 643-656
• Šebestová, Ivana; Dolejší, V.: A posteriori error estimates of the discontinuous Galerkin method for the heat conduction equation. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 53 (2012), issue 1, pp. 77-94
• Rashid, Abdur; Akram, Shakaib: Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction. (English). Applications of Mathematics, vol. 55 (2010), issue 4, pp. 337-350
• Havle, Oto; Dolejší, Vít; Feistauer, Miloslav: Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions. (English). Applications of Mathematics, vol. 55 (2010), issue 5, pp. 353-372
• Lin, Qun; Liu, Tang; Zhang, Shuhua: Superconvergence estimates of finite element methods for American options. (English). Applications of Mathematics, vol. 54 (2009), issue 3, pp. 181-202
• Jia, Shanghui; Li, Deli; Liu, Tang; Zhang, Shuhua: Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media. (English). Applications of Mathematics, vol. 53 (2008), issue 1, pp. 13-39
• Handlovičová, Angela; Mikula, Karol: Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. (English). Applications of Mathematics, vol. 53 (2008), issue 2, pp. 105-129
• Oberhuber, Tomáš: Finite difference scheme for the Willmore flow of graphs. (English). Kybernetika, vol. 43 (2007), issue 6, pp. 855-867
• Krivá, Zuzana: Finite-volume level set method and its adaptive version in completing subjective contours. (English). Kybernetika, vol. 43 (2007), issue 4, pp. 509-522
• Yazaki, Shigetoshi: On the tangential velocity arising in a crystalline approximation of evolving plane curves. (English). Kybernetika, vol. 43 (2007), issue 6, pp. 913-918
• Handlovičová, Angela: Perona-Malik equation: properties of explicit finite volume scheme. (English). Kybernetika, vol. 43 (2007), issue 4, pp. 523-532
• Feistauer, Miloslav; Hájek, Jaroslav; Švadlenka, Karel: Space-time discontinuos Galerkin method for solving nonstationary convection-diffusion-reaction problems. (English). Applications of Mathematics, vol. 52 (2007), issue 3, pp. 197-233
• Lukáčová-Medviďová, Mária; Saibertová-Zatočilová, Jitka: Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics. (English). Applications of Mathematics, vol. 51 (2006), issue 3, pp. 205-228
• Eymard, R.; Gallouët, T.; Herbin, R.; Latché, J.-C.: Analysis tools for finite volume schemes. (English). In: Fila, Marek, Mikula, K. and Quittner, Pavol (eds.): Proceedings of Equadiff 11, International Conference on Differential Equations. Czecho-Slovak series, Bratislava, July 25-29, 2005. [Part 1] Contributions of plenary speakers and minisymposia organizers. Comenius University Press, Bratislava, 2007. pp. 111-136
• Oberhuber, Tomáš: Computational study of the Willmore flow on graphs. (English). In: Fila, Marek, Handlovičová, A., Mikula, K., Medveď, Milan, Quittner, Pavol and Ševčovič, Daniel (eds.): Proceedings of Equadiff 11, International Conference on Differential Equations. Czecho-Slovak series, Bratislava, July 25-29, 2005. [Part 2] Minisymposia and contributed talks. Comenius University Press, Bratislava, 2007. pp. 321-331
• Ferreira, Raúl; de Pablo, Arturo; Pérez-Llanos, Mayte: Numerical blow-up for the $p$-Laplacian equation with a nonlinear source. (English). In: Fila, Marek, Handlovičová, A., Mikula, K., Medveď, Milan, Quittner, Pavol and Ševčovič, Daniel (eds.): Proceedings of Equadiff 11, International Conference on Differential Equations. Czecho-Slovak series, Bratislava, July 25-29, 2005. [Part 2] Minisymposia and contributed talks. Comenius University Press, Bratislava, 2007. pp. 363-367
• Tomoeda, Kenji: Support re-splitting phenomena caused by an interaction between diffusion and absorption. (English). In: Fila, Marek, Handlovičová, A., Mikula, K., Medveď, Milan, Quittner, Pavol and Ševčovič, Daniel (eds.): Proceedings of Equadiff 11, International Conference on Differential Equations. Czecho-Slovak series, Bratislava, July 25-29, 2005. [Part 2] Minisymposia and contributed talks. Comenius University Press, Bratislava, 2007. pp. 499-506
• Kikuchi, N.; Kačur, J.: Convergence of Rothe's method in Hölder spaces. (English). Applications of Mathematics, vol. 48 (2003), issue 5, pp. 353-365
• Faragó, István; Korotov, Sergey; Neittaanmäki, Pekka: Galerkin approximations for the linear parabolic equation with the third boundary condition. (English). Applications of Mathematics, vol. 48 (2003), issue 2, pp. 111-128
• Dolejší, Vít; Feistauer, Miloslav; Felcman, Jiří; Kliková, Alice: Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems. (English). Applications of Mathematics, vol. 47 (2002), issue 4, pp. 301-340
• Becker, Jürgen; Grün, Günther; Lenz, Martin; Rumpf, Martin: Numerical methods for fourth order nonlinear degenerate diffusion problems. (English). Applications of Mathematics, vol. 47 (2002), issue 6, pp. 517-543
• Zlámal, Miloš: Finite element solution of the fundamental equations of semiconductor devices. II. (English). Applications of Mathematics, vol. 46 (2001), issue 4, pp. 251-294
• Říhová-Škabrahová, Dana: Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition. (English). Applications of Mathematics, vol. 46 (2001), issue 2, pp. 103-144
• Angot, Philippe; Dolejší, Vít; Feistauer, Miloslav; Felcman, Jiří: Analysis of a combined barycentric finite volume—nonconforming finite element method for nonlinear convection-diffusion problems. (English). Applications of Mathematics, vol. 43 (1998), issue 4, pp. 263-310
• Lukáčová-Medviďová, Mária: Combined finite element -- finite volume method (convergence analysis). (English). Commentationes Mathematicae Universitatis Carolinae, vol. 38 (1997), issue 4, pp. 717-741
• Lin, Qun; Zhang, Shuhua: A direct global superconvergence analysis for Sobolev and viscoelasticity type equations. (English). Applications of Mathematics, vol. 42 (1997), issue 1, pp. 23-34
• Lukáčová-Medviďová, Mária: Numerical solution of compressible flow. (English). In: Došlá, Z., Kuben, J. and Vosmanský, J. (eds.): Proceedings of Equadiff 9, Conference on Differential Equations and Their Applications, Brno, August 25-29, 1997. [Part 3] Papers. Masaryk University, Brno, 1998. pp. 201-210
• Dalík, Josef; Růžičková, Helena: An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection. (English). Applications of Mathematics, vol. 40 (1995), issue 5, pp. 367-380
• Hlavička, Rudolf: Finite element solution of a hyperbolic-parabolic problem. (English). Applications of Mathematics, vol. 39 (1994), issue 3, pp. 215-239
• Cliffe, K. A.; Garratt, T. J.; Spence, A.: A modified Cayley transform for the discretized Navier-Stokes equations. (English). Applications of Mathematics, vol. 38 (1993), issue 4, pp. 281-288
• Taufer, J.; Vitásek, E.: $A$-stability and numerical solution of abstract differential equations. (English). In: Fábera, Jiří (ed.): Equadiff IV. Czechoslovak Conference on Differential Equations and Their Applications. Proceedings, Prague, August 22-26, 1977. Springer-Verlag, Berlin, 1979. pp. [415]-423
• Rektorys, Karel; Danešová, Jana; Matyska, Jiří; Vitner, Čestmír: Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I. (English). Aplikace matematiky, vol. 22 (1977), issue 5, pp. 349-394
• Rektorys, Karel; Danešová, Jana; Matyska, Jiří; Vitner, Čestmír: Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II. (English). Aplikace matematiky, vol. 22 (1977), issue 6, pp. 425-454
• Gupta, Murli M.: Stability of iterative schemes for nonselfadjoint equations. (English). Aplikace matematiky, vol. 21 (1976), issue 3, pp. 173-184
• Práger, M.; Taufer, J.; Vitásek, E.: Overimplicit methods for the solution of evolution problems. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 125-133
• Rektorys, Karel: Application of the Ritz method to the solution of parabolic boundary value problems of arbitrary order in the space variables. (English). In: Ráb, Miloš and Vosmanský, Jaromír (eds.): Proceedings of Equadiff III. 3rd Czechoslovak Conference on Differential Equations and Their Applications. Brno, Czechoslovakia, August 28 - September 1, 1972. Univ. J. E. Purkyně - Přírodovědecká fakulta, Brno, 1973. pp. 255-260