Partial differential equations · Numerical analysis · Mathematical modeling

Marvin Fritz

Research

Structure-preserving discretization

Many evolution equations encode conservation laws, energy dissipation, positivity, or thermodynamic consistency. I study finite-element and time-stepping methods that preserve these properties at the discrete level, particularly for Cahn–Hilliard-type equations and coupled multiphysics models.

Fractional, nonlocal, and stochastic equations

Fractional derivatives and nonlocal operators describe memory, anomalous diffusion, and long-range interactions. My work addresses well-posedness, energy behaviour, order perturbations, random forcing, and computable approximations for such models.

Control, coupled systems, and nonlinear acoustics

I investigate feedback stabilization and numerical control for nonlinear PDEs, together with coupled systems arising from flow, poroelasticity, transport, and wave propagation. A recurring goal is to connect rigorous stability analysis with implementable algorithms.

Mathematical models in the life sciences

Phase-field, transport, tissue-mechanics, and vascular-network models make it possible to study interacting biological processes across scales. Applications include tumor evolution, angiogenesis, immunotherapy, digit morphogenesis, and biological damage and repair.

Upcoming talks

Preprints

[43] A monotone approach to global weak solutions of the purely elastic Cahn–Hilliard–Biot system
(2026) Submitted Preprint
[42] Generalised dissipative solutions for a non-isothermal phase-field system: existence, weak-strong uniqueness, and long-time behaviour
(2026) Submitted arXiv:2608.26297
[41] High-order conforming finite elements for the Cahn–Hilliard equation: Relative-energy stability and energy defects
(2026) Submitted arXiv:2606.06719
[40] An Allen–Cahn equation with jump-diffusion noise for biological damage and repair processes
(2026) Submitted arXiv:2602.17495
[39] A coercive space-time variational approach to fractional diffusion problems
(2026) Submitted arXiv:2609.00091
[38] A Gronwall framework for order perturbations in multi-term fractional differential equations
(2026) Submitted
[37] A semiconvex counterexample to energy monotonicity for time-fractional gradient flows
(2026) Preprint arXiv:2608.01188
[36] Entropy-consistent edge finite elements for degenerate Cahn–Hilliard flows: Stability and convergence
(2026) Submitted
[35] Global weak solutions of a one-sided degenerate Cahn–Hilliard model for traction-driven digit morphogenesis
(2026) Submitted arXiv:2606.10793
[34] Numerical analysis of an implicit-mobility mass-lumped finite element scheme for the degenerate Cahn–Hilliard equation
(2026) Submitted
[33] On the well-posedness of the 3D Navier–Stokes equations with distributed relaxation viscosity
(2026) Submitted
[32] Sharp CFL stability and adaptivity for explicit Cahn–Hilliard time stepping
(2026) Submitted
[31] Sparse fidelity feedback and spectral design for Cahn–Hilliard image inpainting
(2026) Submitted
[30] Structure-preserving discretization and fingering dynamics of a Cahn–Hilliard model for traction-driven digit morphogenesis
(2026) Submitted arXiv:2606.12574

Refereed articles

[10] Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
Advances in Nonlinear Analysis (2023)

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