Publications - Lubomir Banas

Preprints

L. Banas, M. Roeckner, A. Wilke. Convergent numerical approximation of the stochastic total variation flow with linear multiplicative noise: the higher dimensional case, submitted (2022) preprint.
L. Banas, M. Ondrejat. Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow, M2AN Math. Model. Numer. Anal., accepted, (2022) preprint.
L. Banas, M. Roeckner, A. Wilke. Correction to: Convergent numerical approximation of the stochastic total variation flow, Stoch. Partial Differ. Equ. Anal. Comput., accepted, (2022) preprint.
L. Banas, C. Vieth. Robust a posteriori estimates for the stochastic Cahn-Hilliard equation, Math. Comput., accepted, (2023) preprint.
L. Banas, B. Gess, M. Neuss. Stochastic partial differential equations arising in self-organized criticality, submitted, (2022) preprint.
L. Banas, A. Wilke. A posteriori estimates for the stochastic total variation flow, SIAM J. Numer. Anal., accepted, (2022) preprint.
L. Banas, B. Gess, C. Vieth. Numerical approximation of singular-degenerate parabolic stochastic PDEs, submitted, (2022) preprint.

Journal papers

L. Banas, H. Dawid, T. Randrianasolo, J. Storn, X. Wen. On numerical approximation of a system of Hamilton-Jacobi-Bellman equations arising in innovation dynamics. J. Sci. Comput., published online, (2022) preprint.
L. Banas, H. Yang, R. Zhu. Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise, Potential Anal., published online, (2022) preprint.
L. Banas, R. Lasarzik, A. Prohl. Numerical Analysis for Nematic Electrolytes, IMA J. Numer. Anal., Vol. 41(3), pp. 2186-2254, (2021) preprint.
L. Banas, G. Ferrari, T. Randrianasolo. Numerical approximation of the value of a stochastic differential game with asymmetric information, SIAM J. Control. Optim., Vol. 59(2), pp. 887-905, (2021) preprint.
L. Banas, M. Roeckner, A. Wilke. Convergent numerical approximation of the stochastic total variation flow, Stoch. Partial Differ. Equ. Anal. Comput., Vol. 9, pp. 437-471 (2021) preprint.
D. Antonopoulu, L. Banas, R. Nurnberg, A. Prohl. Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit, Numer. Math., 147, pp. 505-551, (2021) preprint.
L. Banas, H. Mahato. Homogenization of evolutionary Stokes-Cahn-Hilliard Equations for Two-Phase Porous Media Flow, Asymptotic Analysis, 105(1-2), pp. 77-95, (2017) preprint.
L. Banas, R. Nurnberg. Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow, ESAIM: M2AN Math. Model. Numer. Anal., 51(3), pp. 1089-1117, (2017) preprint.
L. Banas, Z. Brzezniak, M. Neklyudov, M. Ondrejat, A. Prohl. Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere, Czechoslovak Mathematical Journal, 65(140), 617-657 (2015) preprint.
L. Banas, M. Page, D. Praetorius. A Convergent Linear Finite Element Scheme for the Maxwell-Landau-Lifshitz-Gilbert Equation, ETNA, 44, 153-176 (2015) preprint.
L. Banas, M. Klein, A. Prohl. Control of interface evolution in multi-phase fluid flows., SIAM J. Control. Optim., 52(4), 2284-2318 (2014) preprint.
L. Banas, M. Page, D. Praetorius, J. Rochat. A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction. , IMA J. Numer. Anal., 34(4), 1361-1385, (2014) preprint.
L. Banas, Z. Brzezniak, M. Neklyudov, A. Prohl. Convergent finite element based discretization of the stochastic Landau-Lifshitz-Gilbert equation. IMA J. Numer. Anal., 34(2), 502-549, (2014), preprint.
L. Banas, A. Novick-Cohen, R. Nurnberg. The degenerate and non-degenerate deep quench obstacle problem: a numerical comparison , Networks and Heterogeneous Media, 8(1), 37-64, (2013), preprint.
L. Banas, Z. Brzezniak, A. Prohl. Computational studies for the stochastic Landau-Lifshitz-Gilbert equation, SIAM J. Sci. Comput., 35(1), B62-B81, (2013). preprint.
L. Banas, A. Prohl, M. Slodicka. Numerical scheme for augmented Landau-Lifshitz equation in heat assisted recording, J. Comput. Appl. Math., 236(18), 4775-4787, (2012) preprint.
L. Banas, A. Prohl. Convergent Finite Element Discretization of the Multi-fluid Nonstationary Incompressible Magnetohydrodynamics Equations, Math. Comput., Volume 79 (2010), Issue 272, 1957-1999, preprint.
L. Banas, A. Prohl, R. Schaetzle. Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii., Numer. Math., Volume 115 (2010), Number 3, Pages 395-432, preprint.
L. Banas. An efficient multigrid preconditioner for Maxwell's equations in micromagnetism, Mathematics and Computers in Simulation, Volume 80 (2010), Pages 1657-1663, preprint.
L. Banas, R. Nurnberg. A multigrid method for the Cahn-Hilliard equation with obstacle potential, Applied Mathematics and Computation, Volume 213 (2009), Issue 2, Pages 290-303, preprint.
L. Banas, R. Nurnberg. A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy, M2AN Math. Model. Numer. Anal., Volume 43 (2009), Issue 5, Pages: 1003-1026, preprint.
L. Banas, R. Nurnberg. Phase field computations for surface diffusion and void electromigration in R³, Comp. Visual. Sci., Volume 12 (2009), Issue 7), Pages 319-327.
L. Banas, A. Prohl, M. Slodicka. Modeling of thermally assisted magnetodynamics, SIAM J. Numer. Anal., Volume 47 (2008), Issue 1, Pages 551-574, preprint.
L. Banas, R. Nurnberg. Finite Element Approximation of a Three Dimensional Phase Field Model for Void Electromigration. J. Sci. Comput., Volume 37 (2008), Issue 2, Pages 202-232, preprint.
L. Banas, S. Bartels, A. Prohl. A convergent implicit finite element discretization of the Maxwell-Landau-Lifshitz-Gilbert equation. SIAM J. Numer. Anal., Vol. 46 (2008), Issue 3, Pages 1399-1422, preprint
L. Banas, R. Nurnberg. Adaptive finite element methods for Cahn-Hilliard equations. J. Comp. Appl. Math., Vol. 218 (2008), Issue 1, Pages 2-11. available online
L. Banas. Adaptive techniques for Landau-Lifshitz-Gilbert equation with magnetostriction. J. Comp. Appl. Math., Vol. 215 (2008), Issue 2, Pages 304-310, available online
L. Banas, M. Slodicka. Error estimates for Landau-Lifshitz-Gilbert equation with magnetostriction. Appl. Numer. Math., Vol. 56, Issue 8 (2006), Pages 1019-1039, available online
L. Banas. A numerical method for the Landau-Lifshitz equation with magnetostriction. Math. Methods Appl. Sci., Vol. 28, Issue 16 (2005), Pages 1939-1954, available online
L. Banas, M. Slodicka. Space discretization for Landau-Lifshitz-Gilbert equation with magnetostriction. Comput. Meth. Appl. Mech. Eng., Vol. 194, Issue 2-5 (2005), 467-477, available online
M. Slodicka, L. Banas. A numerical scheme for a Maxwell-Landau-Lifshitz-Gilbert System. Applied Mathematics and Computation, Vol. 158, Issue 1 (2004), 79-99, available online
L. Banas. Solution of the convection-diffusion equation by the method of characteristics. J. Comp. Appl. Math., Vol. 168, Issue 1-2 (2004), 31-39, available online

Books

L. Banas, Z. Brzezniak, M. Neklyudov, A. Prohl, Stochastic Ferromagnetism: Analysis and Numerics, De Gruyter Studies in Mathematics 58, (2014).

Conference proceedings

L. Banas. Adaptive Methods for Dynamical Micromagnetics. In: A. Bermudez, D. Gomez, P. Quintela, P. Salgado (eds.), Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2005, 18 - 22 July, 2005, Santiago de Compostela, Spain. Pages 531-538, Springer, (2006), ISBN: 978-3-540-34287-8, preprint.
L. Banas. Numerical methods for the Landau-Lifshitz-Gilbert equation. Lecture Notes in Computer Science, Volume 3401, 2005, ISBN: 3-540-24937-0, preprint.

Selected presentations

Sharp interface limit of the numerical approximation of the stochastic Cahn-Hilliard equation. Numerical Methods for SPDE: 20 Successful Years and Future Challenges, Mittag-Leffler Institute, Sweden, May, 2019.
Numerical approximation and optimal control of phase-field models for multiphase flow. 14th International Conference on Free Boundary Problems, Shanghai, July, 2017.
Phase-field models for multiphase flow: numerics and homogenization. MIGSAA Summer school on multiscale problems in nonlinear PDEs, Edinburgh, November 5-7, 2017.
Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp-interface limit. Nonlinear stochastic evolution equations, Berlin, November 3-5, 2016.
Optimal Control of Phase-field Models for Multiphase Flow. ICIAM 2015, Beijing, August 10-14, 2015.
Numerical Approximation of Multicomponent Phase-field Models for Multiphase Flow. ICIAM 2015, Beijing, August 10-14, 2015.
Numerical methods for dynamical micromagnetism. 5th Spring School on Evolution Equations, Berlin, March 11th - 15th, 2013.
A finite element method for a non-smooth phase field model for two-phase fluid flows. ALGORITMY 2009, Podbanske, Slovakia, March 15-20, 2009.
Finite element approximations of some incompresible fluid flow problems Numerical Analysis Seminar, University of Tuebingen, Germany, February 19, 2009.
Finite element approximations of some incompresible fluid flow problems Applied Mathematics Seminar, University of Dundee, UK, February 10, 2009.
A finite element method for the multi-fluid incompressible magnetohydrodynamic equations. Numerical Solution of Complex PDE Systems, 5th MIDNAG Meeting, Leicester, UK, November 19, 2008.
A finite element method for multi-fluid magnetohydrodynamics. Applied mathematics seminar, University of Leeds, Leeds, UK, November 17, 2008.
A phase field model for magnetohydrodynamics. Mathematics seminar, Stirling University, Stirling, UK, September 23, 2008.
On phase field modelling of multi-phase flows. Maxwell Symposium on Computational Mathematics, Edinburgh, UK, November 22, 2007.
A finite element method for a non-smooth phase field model for two-phase fluid flows. Slovak-Austrian Mathematical Congress, Podbanske, Slovakia, September 16-21, 2007.
On multigrid methods for the Cahn-Hilliard equation with obstacle potential. Computational Linear Algebra with Applications, Harrachov, Czech Republic, August 19-25, 2007.
On adaptive multilevel methods for phase field computations. Numerical Analysis Seminar, University of Tuebingen, Germany, May 10, 2007.
Adaptive finite element methods for Cahn-Hilliard equations. FEMTEC 2006, El Paso, USA, December 11-15, 2006.
A numerical method for the degenerate Cahn-Hilliard equation. WCCM 2006, Los Angeles, USA, July 16-22, 2006.
A multigrid method for three dimensional phase field computations. MAFELAP 2006, Uxbridge, UK, June 13-16, 2006.
Adaptive methods for dynamical micromagnetics. ENUMATH 2005, Santiago de Compostela, Spain, July 18-22, 2005.
Computation of deformation and magnetostriction in micromagnetics. 4th FTW PhD Symposium, Gent, Belgium, December 3rd, 2003.
Space discretization for the Landau-Lifshitz-Gilbert equation with magnetostriction. MAFELAP 2003, Uxbridge, UK, June 21-24, 2003.
A numerical method for a micromagnetic model. 3rd FTW PhD Symposium, Gent, Belgium, December 11th, 2002.