Centre of analysis and numerics for fluid-structure interactions at Charles University

News Conferences and talks Publications Preprints

News

2026

• The ERC-CZ project LL2105 CONTACT was successfully completed (1 September 2021 – 31 August 2026). During the project 33 papers were published, 2 more were accepted and 11 preprints are available, see the complete list. The work of the centre continues.
• Congratulations Pei Su for obtaining a permanent position as Maître de Conférences at the Université de Nantes, France.
• Together with the groups of M. Fernández, S. Frei and T. Wick we proposed a numerical benchmark for fluid-structure-contact interaction, arXiv:2609.18854. The benchmark on contactless rebounds was presented at the WCCM-ECCOMAS 2026 in Munich, see Numerics.
• The paper of S. Mosny, B. Muha, S. Schwarzacher and J. T. Webster on time-periodic solutions for hyperbolic-parabolic systems was accepted in the Journal of the European Mathematical Society. The follow-up work of B. Muha, S. Schwarzacher and J. T. Webster shows that its assumptions are qualitatively sharp, arXiv:2609.17712.
• S. Schwarzacher was one of the two main speakers at the Seminar on Differential Equations in Zadov.
• S. Schwarzacher was one of the four main speakers at the EMS school Mathematical Aspects of Fluid Flows in Kácov (May 2026), with a lecture series on fluid-structure interaction.
• S. Schwarzacher became one of the three series editors of Advances in Mathematical Fluid Mechanics and Lecture Notes in Mathematical Fluid Mechanics (Springer/Birkhäuser). The results on elastic shells obtained with P. Su, D. Breit and P. R. Mensah will be collected in a monograph in the series Advances in Mathematical Fluid Mechanics.
• T. Biswas had a research stay at Chungbuk National University, Cheongju, South Korea (February–March 2026), with a seminar talk on fluid-structure interaction with plastic deformation.
• P. Su gave invited talks on the motion of a rigid body in a compressible ideal fluid at the Université Paris-Est Créteil and at the conference ModConFlex in Wuppertal (May–June 2026).
• Welcome back Pei Su, who rejoined the team in January 2026 after her postdoc at the Université Paris-Saclay (Institut de Mathématique d'Orsay). The postdoc positions of T. Biswas and M. Fehling were extended.

2025

• Congratulations Jakub Fara for his successful PhD defense with the thesis „Advanced computational tools for solving fluid-structure interaction problems“.
• Congratulations Malte Kampschulte for obtaining a tenure-track position at the Department of Mathematical Analysis, Charles University.
• Congratulations Marc Fehling for winning the SIAM/ACM Prize in Computational Science and Engineering as one of the principal authors of the deal.II project.
• Regular meetings of an international group prepared a numerical benchmark on the contactless rebound of an elastic ball in a fluid.

2024

• Congratulations Antonín Češík and Claudiu Mîndrilă for their successful PhD defenses. A. Češík continues as a postdoc at the University of Warwick, C. Mîndrilă as a postdoc at BCAM, Bilbao.
• The conference Modelling, PDE Analysis and Computational Mathematics in Materials Science (MPDE 2024) took place in Prague, 22–27 September 2024, with about 80 participants.
• Welcome to the two new postdocs Tania Biswas and Marc Fehling.
• Mid-term review of the project (14 March 2024): the evaluation panel of the Ministry rated the project A1 – the project successfully fulfils its aims; excellent research results of international significance.
• M. Kampschulte took a substitute professorship in Leipzig and P. Su a postdoc position at the Université Paris-Saclay.

2023

• We welcome the new faculty member Daniel Campbell and the new PhD students Jakub Cach (supervision of K. Tůma) and Stanislav Mosny (supervision of S. Schwarzacher at the University of Uppsala) to the team.

2022

• Congratulations Sebastian Schwarzacher for his habilitation at Charles University (November 2022).
• Welcome to the new postdocs Pei Su (from February 2022), Joonas Niinikoski (from April 2022) and Bangwei She (from July 2022).

2021

• Start of the ERC-CZ project LL2105 CONTACT (1 September 2021).

Conferences and talks 2021–2026

Number of presentations of team members according to the final report of the project:

2026

• EMS school Mathematical Aspects of Fluid Flows, Kácov, May 2026: lecture series of S. Schwarzacher as one of the four main speakers.
• Seminar on Differential Equations, Zadov: S. Schwarzacher as one of the two main speakers.
• AIMS 2026, Athens: two invited talks of S. Schwarzacher, invited talk of M. Kampschulte.
• CMAM 2026, Vienna: invited talk of S. Schwarzacher.
• EQUADIFF 2026, Prague: invited talks of B. Benešová, M. Kampschulte and K. Tůma.
• WCCM-ECCOMAS 2026, Munich: invited talks of S. Schwarzacher and K. Tůma. The benchmark on contactless rebounds was presented in the minisymposium organised by M. Fernández and H. van Brummelen.
• Conference „New Paths in the PDEs of Fluid Mechanics“, Peyresq (Alpes-de-Haute-Provence, France), 31 August – 4 September 2026: invited talk of S. Schwarzacher.
• ModConFlex, Wuppertal, and Université Paris-Est Créteil: invited talks of P. Su.
• Chungbuk National University, Cheongju, South Korea: seminar talk of T. Biswas during her research stay (February–March 2026).
• Further participation: CSASC 2026, Pilsen (S. Schwarzacher); Junior PDE Workshop, Paris (P. Su); EMS school in Kácov (P. Su).
• 17th International Conference on Free Boundary Problems, Berlin, 7–11 September 2026: Y. Liu, I. Kukavica and S. Schwarzacher organized a minisymposium on fluid-structure interactions.

2025

• Brijuni Applied Mathematics Workshop 2025, Brijuni, Croatia, 23–27 June 2025: specialised meeting on fluid-structure interaction organized by M. Galić, I. Kukavica, B. Muha and S. Schwarzacher; talks of S. Schwarzacher and M. Fehling.
• ECCOMAS conference 2025, Heidelberg: S. Schwarzacher and T. Richter organized a minisymposium combining theory and numerics of fluid-structure interaction; talks of M. Fehling and K. Tůma.
• Erwin Schrödinger Institute (ESI), Vienna: invited talk of S. Schwarzacher.
• 3rd Czech-Chinese conference: invited talks of M. Kampschulte and K. Tůma.

2024

• Modelling, PDE Analysis and Computational Mathematics in Materials Science (MPDE 2024), Prague, 22–27 September 2024, organized by M. Bulíček, J. Málek, V. Průša, S. Schwarzacher and E. Süli (about 80 participants). Six team members gave talks and two presented posters:
  • B. Benešová: Linearization in elastodynamics (talk)
  • J. Cach: Flow around an obstacle: Various approaches to calculate pointwise traction (talk)
  • J. Fara: Remeshing strategy in ALE method: Contactless rebound simulation (talk)
  • M. Kampschulte: Variational aspects of fluid-structure interaction (talk)
  • P. Su: Conditional regularity for an elastic shell interacting with the Navier-Stokes equations (talk)
  • K. Tůma: Efficient linear semi-implicit finite element scheme for fluid-shell interaction (talk)
  • D. Campbell: Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity (poster)
  • M. Fehling: Massively parallel hp-adaptive finite element methods (poster)
• Annual meeting of the GAMM Activity Group „Analysis of Partial Differential Equations“, Prague, 16–19 September 2024, organized by B. Benešová, M. Kružík and S. Schwarzacher; M. Kampschulte invited speaker.

2023

• ICIAM 2023, Tokyo: B. Muha, J. Webster and S. Schwarzacher organized the minisymposium Bifurcations, periodicity and stability in fluid-structure interactions. M. Kampschulte was invited speaker at the minisymposium Interfaces and Free Boundaries in Fluid Mechanics and Materials Science.
• Workshop Recent Progress in Deterministic and Stochastic Fluid-Structure Interaction, SLMath (MSRI), Berkeley: invited talk of S. Schwarzacher.
• RIMS workshop, Kyoto: invited talk of S. Schwarzacher.
• Workshop Between Regularity and Defects: Variational and Geometrical Methods in Materials Science, Erwin Schrödinger Institute, Vienna: invited talks of B. Benešová and S. Schwarzacher.
• Workshop Nonlinear PDEs: Recent Trends in the Analysis of Continuum Mechanics, Hausdorff Center for Mathematics, Bonn: invited talks of B. Benešová and S. Schwarzacher.
• Further conferences and schools with participation of team members (travel funded by the project): GAMM Annual Meeting, Dresden (M. Kampschulte); GeoCa 2023, Lysečiny (A. Češík, M. Kampschulte); ENUMATH 2023, Lisbon (K. Tůma); FEniCS 2023, Cagliari (J. Fara); Tenth Congress of Romanian Mathematicians, Pitești (C. Mîndrilă); Variational Models in Materials Science, Naples (B. Benešová); 32nd Jyväskylä Summer School (A. Češík); PDEs and Applications seminar, Uppsala (A. Češík).

2022

• EQUADIFF 15, Brno: S. Schwarzacher organized the minisymposium PDE-02 Analysis for fluid-structure interactions.
• ApplMath 2022, Croatia: minisymposium organized by S. Schwarzacher.
• Workshop „Analysis of Fluid and Elastic Bodies Interactions“, Regensburg: plenary talk of S. Schwarzacher.
• Institut Mittag-Leffler: invited talk of S. Schwarzacher.
• SIAM Conference on Analysis of Partial Differential Equations (PD22), virtual: M. Kampschulte spoke in the minisymposium MS103 Free Boundaries in Fluids and Fluid-Structure Interactions, S. Schwarzacher in MS21 Nonlinear Effects in Fluid Dynamics and MS71 On Fluid-Structure Interactions and Related Problems.

2021

• Lake Como School: invited lecture of S. Schwarzacher.
• BIRS workshop, Banff: talk of S. Schwarzacher.

Publications of the ERC-CZ project

Complete list according to the final report of the project: 33 published papers, 2 accepted papers and 11 preprints (46 outputs in total).

Accepted for publication (2)

1. S. Mosny, B. Muha, S. Schwarzacher, J. T. Webster: Time-Periodic Solutions for Hyperbolic-Parabolic Systems. Accepted for publication in Journal of the European Mathematical Society (2026). arXiv:2412.18801.
2. D. Arndt, W. Bangerth, B. Blais, M. Fehling, R. Gassmöller, T. Heister, L. Heltai, V. Ivannikov, M. Kronbichler, M. Maier, P. Munch, A. Steger, D. Still, B. Turcksin, D. Wells: The deal.II Library, Version 9.8. Accepted for publication in Journal of Numerical Mathematics (2026). DOI: 10.1515/jnma-2026-0118.

2026 (5 papers)

1. S. Almi, R. Badal, M. Friedrich, S. Schwarzacher: Thermo-elastodynamics of nonlinearly viscous solids. Calculus of Variations and Partial Differential Equations 65 (2026), Article 111. DOI: 10.1007/s00526-026-03282-9.
2. D. Campbell, L. D’Onofrio, T. Vítek: Diffeomorphic Approximation of Piecewise Affine Homeomorphisms. The Journal of Geometric Analysis 36 (2026), Article 157. DOI: 10.1007/s12220-026-02398-w.
3. D. Campbell: A Note on Sobolev-Lorentz Capacity and Hausdorff Measure. Mathematische Nachrichten 299(7) (2026), 1540–1548. DOI: 10.1002/mana.70157.
4. W. N. Munshi, M. Fehling, W. Bangerth, C. Annavarapu: A detailed guide to an open-source implementation of the hybrid phase field method for 3D fracture modeling in deal.II. Computer Physics Communications 319 (2026), 109901. DOI: 10.1016/j.cpc.2025.109901.
5. M. Bag, T. Biswas, S. Dharmatti: On the Cahn-Hilliard-Navier-Stokes equations with nonhomogeneous boundary. Journal of Elliptic and Parabolic Equations (2026). DOI: 10.1007/s41808-026-00497-x.

2025 (13 papers)

1. P. Su, C. Sun, X. Yuan: Quantitative observability for one-dimensional Schrödinger equations with potentials. Journal of Functional Analysis 288 (2025), 110695.
2. J. He, P. Su: The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid. Mathematische Annalen 391 (2025), 5341–5373.
3. A. Češík, G. Gravina, M. Kampschulte: Inertial (self-)collisions of viscoelastic solids with Lipschitz boundaries. Advances in Calculus of Variations 18(2) (2025), 439–466.
4. A. Češík, S. Schwarzacher: Stability and convergence of in time approximations of hyperbolic elastodynamics via stepwise minimization. Journal of Differential Equations 415 (2025), 434–486. Paper.
5. S. Schwarzacher, B. She, K. Tůma: Stability and error estimates of a linear numerical scheme approximating nonlinear fluid–structure interactions. Numerische Mathematik 157 (2025), 1023–1077. Paper.
6. S. Schwarzacher, P. Su: Existence of Strong Solutions for a Perfect Elastic Beam Interacting with Navier–Stokes Equations. Communications in Mathematical Physics 406 (2025), Article 206. Paper.
7. D. Campbell, S. Hencl, A. Menovschikov, S. Schwarzacher: Injectivity in second-gradient nonlinear elasticity. Calculus of Variations and Partial Differential Equations 64 (2025), Article 256. Paper.
8. D. Breit, S. Schwarzacher: The Stokes problem with Navier boundary conditions in irregular domains. Calculus of Variations and Partial Differential Equations 64 (2025), Article 304. Preprint.
9. D. Breit, P. R. Mensah, S. Schwarzacher, P. Su: Ladyzhenskaya–Prodi–Serrin condition for fluid-structure interaction systems. Annali della Scuola Normale Superiore di Pisa – Classe di Scienze (2025). DOI: 10.2422/2036-2145.202407_010.
10. B. Benešová, Š. Nečasová, J. Scherz, A. Schlömerkemper: A variational approach to the modeling of compressible magnetoelastic materials. Journal of the Mechanics and Physics of Solids 201 (2025), 106169.
11. D. Campbell: Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity. Advances in Calculus of Variations 18(3) (2025), 689–729.
12. D. Campbell, A. Kauranen, E. Radici: Classification of area-strict limits of planar BV homeomorphisms. Journal of the London Mathematical Society 111(6) (2025), e70172.
13. D. Arndt, W. Bangerth, M. Bergbauer, B. Blais, M. Fehling, R. Gassmöller, T. Heister, L. Heltai, M. Kronbichler, M. Maier, P. Munch, S. Scheuerman, B. Turcksin, S. Uzunbajakau, D. Wells, M. Wichrowski: The deal.II Library, Version 9.7. Journal of Numerical Mathematics 33(4) (2025), 403–415. DOI: 10.1515/jnma-2025-0115.

2024 (8 papers)

1. A. Češík, G. Gravina, M. Kampschulte: Inertial evolution of non-linear viscoelastic solids in the face of (self-)collision. Calculus of Variations and Partial Differential Equations 63 (2024), Article 55. Paper.
2. D. Breit, M. Kampschulte, S. Schwarzacher: Compressible fluids interacting with 3D visco-elastic bulk solids. Mathematische Annalen 390 (2024), 5495–5552. Paper.
3. J. Fara, S. Schwarzacher, K. Tůma: Geometric re-meshing strategies to simulate contactless rebounds of elastic solids in fluids. Computer Methods in Applied Mechanics and Engineering 422 (2024), 116824. Paper.
4. B. Benešová, M. Kampschulte, S. Schwarzacher: A variational approach to hyperbolic evolutions and fluid-structure interactions. Journal of the European Mathematical Society 26 (2024), 4615–4697. Paper.
5. M. Kampschulte, B. Muha, S. Trifunović: Global weak solutions to a 3D/3D fluid-structure interaction problem including possible contacts. Journal of Differential Equations 385 (2024), 280–324. Paper.
6. V. Julin, J. Niinikoski: Consistency of the flat flow solution to the volume preserving mean curvature flow. Archive for Rational Mechanics and Analysis 248 (2024), Article 1.
7. A. Češík: Convex hull property for elliptic and parabolic systems of PDE. Nonlinear Analysis 245 (2024), 113554. Preprint.
8. P. C. Africa, D. Arndt, W. Bangerth, B. Blais, M. Fehling, R. Gassmöller, T. Heister, L. Heltai, S. Kinnewig, M. Kronbichler, M. Maier, P. Munch, M. Schreter-Fleischhacker, J. P. Thiele, B. Turcksin, D. Wells, V. Yushutin: The deal.II Library, Version 9.6. Journal of Numerical Mathematics 32(4) (2024), 369–380. DOI: 10.1515/jnma-2024-0137.

2023 (5 papers)

1. B. Benešová, M. Kampschulte, S. Schwarzacher: Variational methods for fluid–structure interaction and porous media. Nonlinear Analysis: Real World Applications 71 (2023), 103819. Paper.
2. M. Rezaee-Hajidehi, K. Tůma, S. Stupkiewicz: Indentation-induced martensitic transformation in SMAs: Insights from phase-field simulations. International Journal of Mechanical Sciences 245 (2023), 108100. Paper.
3. M. Kampschulte, S. Schwarzacher, G. Sperone: Unrestricted deformations of thin elastic structures interacting with fluids. Journal de Mathématiques Pures et Appliquées 173 (2023), 96–148. Paper.
4. O. Saari, S. Schwarzacher: Construction of a right inverse for the divergence in non-cylindrical time dependent domains. Annals of PDE 9 (2023), Article 8. Paper.
5. D. Breit, S. Schwarzacher: Navier–Stokes–Fourier fluids interacting with elastic shells. Annali della Scuola Normale Superiore di Pisa – Classe di Scienze 24 (2023), 619–690. Preprint.

2022 (2 papers)

1. G. Gravina, S. Schwarzacher, O. Souček, K. Tůma: Contactless rebound of elastic bodies in a viscous incompressible fluid. Journal of Fluid Mechanics 942 (2022), A34. Paper.
2. R. Chabiniok, J. Hron, A. Jarolímová, J. Málek, K. R. Rajagopal, K. Rajagopal, H. Švihlová, K. Tůma: Three-dimensional flows of incompressible Navier–Stokes fluids in tubes containing a sinus, with varying slip conditions at the wall. International Journal of Engineering Science 180 (2022), 103749.

Preprints (11)

1. C. Mîndrilă, S. Schwarzacher: Time-periodic weak solutions for the interaction of an incompressible fluid with a linear Koiter type shell under dynamic pressure boundary conditions. arXiv:2303.13625.
2. M. Kampschulte, J. Niinikoski, S. Schwarzacher: Regularity estimates of a fluid-free surface evolution. arXiv:2411.06940.
3. N. Evseev, M. Kampschulte, A. Menovschikov: Zero-extension convergence and Sobolev spaces on changing domains. arXiv:2411.10827.
4. J. Cach, K. Tůma, J. Blechta, S. Schwarzacher: On bifurcations and traction forces on an obstacle in incompressible flow. arXiv:2512.15424.
5. S. Mitra, S. Schwarzacher: Thermal effects in fluid structure interactions. arXiv:2510.04801.
6. B. Benešová, M. Kampschulte, M. Kružík: On the passage from nonlinear to linearized viscoelastodynamics. arXiv:2603.02988.
7. A. Češík, M. Kampschulte, S. Schwarzacher: Fluid-Structure interactions with Navier- and full-slip boundary conditions. arXiv:2603.12030.
8. D. Breit, P. R. Mensah, S. Schwarzacher, P. Su: Well-posedness theorems in fluid-structure interaction: perfectly elastic shells. arXiv:2605.14357.
9. P. Munch, M. Fehling, M. Kronbichler, N. Margenberg, L. P. Saavedra: Solving the (Navier-)Stokes equations with space and time adaptivity using deal.II. arXiv:2603.29621.
10. B. Muha, S. Schwarzacher, J. T. Webster: Range Failure, Resolvent Growth, and Resonance in Partially Dissipative Systems. arXiv:2609.17712.
11. D. Corti, J. Fara, M. A. Fernández, S. Frei, T. Knoke, S. Schwarzacher, K. Tůma, T. Wick: A numerical benchmark for fluid–structure–contact interaction. arXiv:2609.18854.