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Summary:
In this project we consider the numerical approximation of stochastic partial differential equations (SPDEs) and stochastic differential games. For both problems we will address the following aspect of numerical approximation: construction of robust, reliable, structure preserving numerical schemes, analysis of convergence and stability of these numerical schemes and their practical implementation. In addition, we will perform numerical simulations to examine the performance of the developed numerical algorithms and to provide insight into the qualitative and quantitative behavior of the considered systems.
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20107
Christian Vieth, L’ubomír Baňas, Benjamin Gess PDF
Numerical approximation of singular-degenerate parabolic stochastic PDEs Published: IMA J. Numer. Anal. 44, no. 4 (2024), 2090–2137 (2017) |
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20106
Wolf-Jürgen Beyn, Thorsten Hüls PDF
Angular values of nonautonomous linear dynamical systems II -- Reduction theory and algorithm Published: SIAM Journal on Applied Dynamical Systems 22 (2023), 161–195 |
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20105
Wolf-Jürgen Beyn, Gary Froyland, Thorsten Hüls PDF
Angular values of nonautonomous and random linear dynamical systems I: fundamentals Published: SIAM Journal on Applied Dynamical Systems 21 (2022), 1245–1286 |
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20097
Xingang Wen, L’ubomír Baňas, Herbert Dawid, Tsiry Avisoa Randrianasolo, Johannes Storn PDF
Published: Journal of Scientific Computing 92, no. 54 (2022) Notes: DOI: 10.1007/s10915-022-01892-x
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On numerical approximation of a system of Hamilton-Jacobi-Bellman equations arising in innovation dynamics |
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20025
Erika Hausenblas, Tsiry Avisoa Randrianasolo, Mechthild Thalhammer PDF
Project: B3 Published: Journal of Computational and Applied Mathematics 364 (2020), 112335: 1–47
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Theoretical study and numerical simulation of pattern formation in the deterministic and stochastic Gray-Scott equations |
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20007
L’ubomír Baňas, Giorgio Ferrari, Tsiry Avisoa Randrianasolo PDF
Numerical approximation of the value of a stochastic differential game with asymmetric information Published: SIAM Journal on Control and Optimization 59, no. 2 (2021), 1109-1135
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Numerical approximation of the value of a stochastic differential game with asymmetric information |
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19111
L’ubomír Baňas, Huanyu Yang, Rongchan Zhu PDF
Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise Published: Potential Analysis 59 (2023), 497–51 |
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19033
L’ubomír Baňas, Michael Röckner, Andre Wilke PDF
Convergent numerical approximation of the stochastic total variation flow Published: Stochastics and Partial Differential Equations: Analysis and Computations 9, no. 2 (2021), 437–471 |
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19029
Dimitra Antonopoulou, L’ubomír Baňas, Robert Nürnberg, Andreas Prohl PDF
Numerical Approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit Project: B3 Published: Numerische Mathematik 147, no. 3 (2021), 505-551 |
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18016
Tsiry Avisoa Randrianasolo, Erika Hausenblas PDF
Time-Discretization of Stochastic 2-D Navier-Stokes Equations with Penalty-Projection Method Project: B3 Published: Numerische Mathematik 143 (2019), 339–378 |
