Preprints

• L. Banas, J.D. Mukam. Numerical approximation of the stochastic Cahn-Hilliard equation with space-time white noise near the sharp interface limit, submitted (2024) preprint.
• 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, S. Herr. Numerical approximation of bi-harmonic wave maps into spheres, SIAM J. Numer. Anal., accepted (2025) preprint.

Journal papers

• L. Banas, G. Ferrari, T. Randrianasolo. Numerical approximation of Dynkin games with asymmetric information, SIAM J. Control. Optim., 63(1), pp. 256-291 (2025) preprint.
• L. Banas, B. Gess, M. Neuss. Stochastic partial differential equations arising in self-organized criticality, Ann. Appl. Probab., 35(1), pp. 481-522 (2025) preprint.
• L. Banas, J.D. Mukam. Improved estimates for the sharp interface limit of the stochastic Cahn-Hilliard equation with space-time white noise, Interfaces Free Bound., 26(4), pp. 563-586 (2024) preprint.
• L. Banas, C. Vieth. Robust a posteriori estimates for the stochastic Cahn-Hilliard equation, Math. Comput., 92(343), pp. 2025-2063, (2023) preprint.
• L. Banas, B. Gess, C. Vieth. Numerical approximation of singular-degenerate parabolic stochastic PDEs, IMA J. Numer. Anal., 44(4), pp. 2090-2137 (2024) preprint.
• L. Banas, M. Roeckner, A. Wilke. Correction to: Convergent numerical approximation of the stochastic total variation flow, Stoch. Partial Differ. Equ. Anal. Comput., 11(4), pp. 1732-1739 (2023) preprint.
• L. Banas, M. Ondrejat. Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow, M2AN Math. Model. Numer. Anal., Vol 57(2), pp. 785-815, (2022) preprint.
• L. Banas, A. Wilke. A posteriori estimates for the stochastic total variation flow, SIAM J. Numer. Anal., Vol. 60(5), pp. 2657-2680 (2022) preprint.
• 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., Vol. 93, article no. 54, (2022) preprint.
• L. Banas, H. Yang, R. Zhu. Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise, Potential Anal., 59(2), pp. 497-518 (2023) 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., 9(2), 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.