Preprints

Recent preprints by members of the Numerical Analysis Groups.

2026#

Balázs Kovács, Buyang Li, Christian Lubich, Structure-preserving Lagrange-multiplier methods for mean curvature flow and their error bounds, July 2026.
Yanyan Shi, Christian Lubich, Weighted finite difference methods for a nonlinear Klein-Gordon equation with high oscillations in space and time, February 2026.

2025#

Yanyan Shi, Christian Lubich, Weighted finite difference methods for the semiclassical nonlinear Schrödinger equation with multiphase oscillatory initial data, August 2025. To appear in Math. Comp.
Christian Lubich, Jörg Nick, Regularized dynamical parametric approximation of stiff evolution problems, January 2025.

2024#

Michael Feischl, Caroline Lasser, Christian Lubich, Jörg Nick, Regularized dynamical parametric approximation, March 2024, revised March 2026. To appear in Numer. Math.
Max Jensen, Fabian Merle, Andreas Prohl, Data-dependent density estimation for the Fokker-Planck equation in higher dimensions, January 2024.

2022#

Andreas Prohl, Fabian Merle, A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems, May 2022.
Xiaobing Feng, Akash A. Panda, Andeas Prohl, Higher order time discretization for the stochastic semilinear wave equation with multiplicative noise, May 2022.

2021#

Fabian Merle, Andreas Prohl, An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems, March 2021.

2020#

Andreas Prohl, Yanqing Wang, Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise, November 2020.
Cedric Beschle, Balázs Kovács, Error estimates for general non-linear Cahn–Hilliard equations on evolving surfaces, June 2020.
Paula Harder, Balázs Kovács, Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions, June 2020.
Jan Bohn, Michael Feischl, Balázs Kovács, FEM–BEM coupling for Maxwell–Landau–Lifshitz–Gilbert equations via convolution quadrature: Weak form and numerical approximation, March 2020, revised May 2020.
Xiaobing Feng, Andreas Prohl, Liet Vo, Optimally convergent mixed finite element methods for the stochastic Stokes equations, May 2020.
Ľubomír Baňas, Robert Lasarzik, Andreas Prohl, Numerical Analysis for Nematic Electrolytes, April 2020.
Martin Ondreját, Andreas Prohl, Noel J. Walkington, Numerical Approximation of Nonlinear SPDE’s, March 2020.
Andreas Prohl, Yanqing Wang, Strong Rates of Convergence for Space-Time Discretization of the Backward Stochastic Heat Equation, and of a Linear-Quadratic Control Problem for the Stochastic Heat Equation, January 2020.

2019#

Ananta K. Majee, Andreas Prohl, A posteriori error estimation and space-time adaptivity for a linear stochastic PDE with additive noise, November 2019.
Dominik Edelmann, Finite element analysis for a diffusion equation on a harmonically evolving domain, August 2019, revised September 2020.
Dimitra Antonopoulou, Ľubomír Baňas, Robert Nürnberg, Andreas Prohl, Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit, May 2019.
David Hipp, Balázs Kovács, Finite element error analysis of wave equations with dynamic boundary conditions: $L^2$ estimates, January 2019, revised June, December 2019. To appear in IMA J. Numer. Anal.

2018#

Max Jensen, Ananta K. Majee, Andreas Prohl, Christian Schellnegger, Dynamic Programming for Finite Ensembles of Nanomagnetic Particles, June 2018.
Andreas Prohl, Christian Schellnegger, Adaptive concepts for stochastic partial differential equations, February 2018.

2017#

Thomas Dunst, Ananta K Majee, Andreas Prohl, Guy Vallet, On Stochastic Optimal Control in Ferromagnetism, February 2017.

2016#

Balázs Kovács, Computing arbitrary Lagrangian Eulerian maps for evolving surfaces, December 2016, revised March 2017. To appear in NMPDE. doi: 10.1002/num.22340
Ananta K Majee, Convergence of a flux-splitting finite volume scheme for conservation laws driven by Lévy noise, October 2016.
Thomas Dunst, Andreas Prohl, Stochastic optimal control of finite ensembles of nanomagnets, June 2016.
Ujjwal Koley, Ananta K Majee, Guy Vallet, [A Finite difference scheme for conservation laws driven by Lévy noise](/pub/majee/rate of convergence_final_v2.pdf), May 2016.
Ujjwal Koley, Ananta K Majee, Guy Vallet, Continuous dependence estimate for a degenerate parabolic-hyperbolic equation with Lévy noise, May 2016, revised October 2016. To appear in Stoch PDE: Anal Comp.
Imran H Biswas, Ananta K Majee, Guy Vallet, On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise, April 2016.
Janos Karátson, Balázs Kovács, Sergey Korotov, Discrete maximum principles for nonlinear elliptic finite element problems on Riemannian manifolds with boundary, February 2016, revised December 2016. To appear in IMA J. Numer. Anal. doi: 10.1093/imanum/dry086
Bernd Brumm, A fast matrix-free spectral method for the nonlinear Schrödinger equation, January 2016.

2015#

Buyang Li, Convergence of a decoupled mixed FEM for the dynamic Ginzburg–Landau equations in nonsmooth domains with incompatible initial data, September 2015.
Jonathan Seyrich, A splitting integrator for the BCS equations of superconductivity, May 2015.
Thomas Dunst, Andreas Prohl, The forward-backward stochastic heat equation: numerical analysis and simulation, May 2015.

2014#

Andreas Prohl, Strong rates of convergence for a space-time discretization of the stochastic Allen-Cahn equation with multiplicative noise, December 2014.
Markus Klein, Andreas Prohl, Optimal control for the thin-film equation: Convergence of a multi-parameter approach to track state constraints avoiding degeneracies, October 2014.
Chuchu Chen, Jialin Hong, Andreas Prohl, Convergence of a θ-scheme to solve the stochastic nonlinear Schrodinger equation with Stratonovich noise, October 2014.

2013#

Thomas Dunst, Markus Klein, Andreas Prohl, Ailyn Schäfer, Optimal Control in Evolutionary Micromagnetism, July 2013.
Xiaobing Feng, Yukun Li, Andreas Prohl, Finite element approximations of the stochastic mean curvature flow of planar curves of graphs, March 2013.

2012#

Heiko Kröner, An inverse curvature flow in a spacetime with a future singularity, November 2012.
Heiko Kröner, A note on inverse mean curvature flow in cosmological spacetimes, November 2012.
Ľubomír Baňas, Zdzislaw Brzeźniak, Mikhail Neklyudov, Andreas Prohl, Convergent Finite Element Based Discretization of the Stochastic Landau-Lifshitz-Gilbert Equation, October 2012.
Ľubomír Baňas, Markus Klein, Andreas Prohl, Control of Interface Evolution in Multi-Phase Fluid Flows, October 2012, revised July 2013.

2011#

Mikhail Neklyudov, Andreas Prohl, The role of noise in finite ensembles of nanomagnetic particles, October 2011.
Erich Carelli and Andreas Prohl, Rates of Convergence For Discretisations of Stochastic Incompressible Navier-Stokes Equations, August 2011.
Ľubomír Baňas, Zdzislaw Brzeźniak, Martin Ondreját, Andreas Prohl, Attractivity, Invariance and Ergodicity For SDEs On Riemannian Manifolds, January 2011.

2010#

Thomas Dunst, Erika Hausenblas, Andreas Prohl, Approximate Euler Method For Parabolic Stochastic Partial Differential Equations Driven by Space-Time Lévy Noise, December 2010.
Zdzislaw Brzeźniak, Erich Carelli, Andreas Prohl, Finite Element Based Discretizations of the Incompressible Navier-Stokes Equations With Multiplicative Random Forcing, June 2010.
David Hilditch, Ronny Richter, Hyperbolic formulations of General Relativity with Hamiltonian structure, February 2010.

2009#

Ľubomír Baňas, Zdzislaw Brzeźniak, Andreas Prohl, Convergent Finite Element Based Discretization of the Stochastic Landau-Lifshitz-Gilbert Equations, December 2009.
Erich Carelli, Erika Hausenblas, Andreas Prohl, Time-splitting methods to solve the stochastic incompressible stokes equation, December 2009.
Ľubomír Baňas, Andreas Prohl, Convergent Finite Element Discretization of the Multi-fluid Nonstationary Incompressible Magnetohydrodynamics Equations, April 2009.
Erich Carelli, Alexander Müller, Andreas Prohl, Domain Decomposition Strategies For the Stochastic Heat Equation, April 2009.
Ronny Richter, Strongly hyperbolic Hamiltonian systems in numerical relativity: Formulation and symplectic integration, February 2009.

2008#

Andreas Prohl, Katja Wolf, Convergent Finite Element Discretization of the Navier-Stokes Korteweg System For Liquid-Vapor Phase Transition, July 2008.
Andreas Prohl, Markus Schmuck, Convergent Finite Element Discretizations of the Navier-Stokes-Nernst-Planck-Poisson System, July 2008.
Ľubomír Baňas, Andreas Prohl, and Reiner Schätzle, Finite Element Approximations of Harmonic Map Heat Flows and Wave Map into Spheres of Nonconstant Radii, June 2008.
Ronny Richter, Jörg Frauendiener, Discreted ifferential forms for cosmological space-times, May 2008.
Matthias Loy, Splitting integrators for skew-hermitian systems of stochastic differential equations, March 2008.
Andreas Prohl, Convergent Finite Element Discretizations of the Nonstationary Incompressible Magnetohydrodynamics System, March 2008.

2007#

Erich Carelli, Finite Element Discretization of Motions of Incompressible Generalized Newtonian Flows, December 2007.
Erich Carelli, Andreas Prohl, A Note On Pressure Approximation of First and Higher Order Projection Schemes For the Nonstationary Incompressible Navier-Stokes Equations, December 2007.
Andreas Prohl, Isabelle Weindl, Convergence of an Implicit Finite Element Discretization for a Class of Parabolic Equations With Nonstandard Anisotropic Growth Conditions, November 2007.
Markus Schmuck, Analysis of the Navier-Stokes-Nernst-Planck-Poisson System, November 2007.
Andreas Prohl, Markus Schmuck, Convergent Discretizations for the Nernst-Planck-Poisson System, November 2007.
Andreas Prohl, On Pressure Approximation via Projection Methods for nonstationary incompressible Navier-Stokes Equations, July 2007.
Ľubomír Baňas, Andreas Prohl, and Marián Slodička, Modelling of thermally assisted magnetodynamics, June 2007.
Andreas Prohl, Convergence of a Finite Element based Space-Time Discretization in Elastodynamics, March 2007.
Ľubomír Baňas, Sören Bartels, and Andreas Prohl, A convergent implicit discretization of the Maxwell-Landau-Lifshitz-Gilbert equation, February 2007.
Roland Becker, Xiaobing Feng, Andreas Prohl, Finite element approximations of the Ericksen-Lesie model for nematic liquid crystal flow, January 2007.

2006#

Xiaobing Feng, Michael Neilan, Andreas Prohl, Error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity, September 2006.
Sören Bartels, Xiaobing Feng, Andreas Prohl, Finite Element approximations of wave maps into spheres, June 2006.
Sören Bartels, Andreas Prohl, Fully Practical, Constraint Preserving, Implicit Approximation of Harmonic Map Heat Flow Into Spheres, February 2006.
Sören Bartels, Andreas Prohl, Convergence of an Implicit, Constraint Preserving Finite Element Discretization of p-Harmonic Heat Flow Into Spheres, February 2006.
Sören Bartels, Andreas Prohl, Stable Discretization of Scalar and Constrained Vectorial Perona-Malik Equation, February 2006.