Partial differential equations · Numerical analysis · Mathematical modeling

Marvin Fritz

Marvin Fritz is a tenure-track Professor at the University of Vienna.

My research concerns the analysis and numerical approximation of nonlinear, fractional, nonlocal, and stochastic partial differential equations. A central theme is the development of reliable computational methods that preserve the mathematical structure of models arising in materials science, control, mechanics, nonlinear acoustics, and mathematical biology.

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.

Upcoming talks

Preprints

[38] Numerical analysis of an implicit-mobility mass-lumped finite element scheme for the degenerate Cahn–Hilliard equation
Submitted
[37] Sharp CFL stability and error analysis for fully explicit Cahn–Hilliard time stepping
Submitted
[36] A Gronwall framework for order perturbations in multi-term fractional differential equations
Submitted
[35] Threshold dynamics for subdiffusive grain growth
Submitted
[34] On the well-posedness of the 3D Navier–Stokes equations with distributed relaxation viscosity
Submitted
[33] A semiconvex counterexample to energy monotonicity for time-fractional gradient flows
Preprint arXiv:2608.01188
[32] Global weak solutions of a one-sided degenerate Cahn–Hilliard model for traction-driven digit morphogenesis
Submitted arXiv:2606.10793
[31] Structure-preserving discretization and fingering dynamics of a Cahn–Hilliard model for traction-driven digit morphogenesis
Submitted arXiv:2606.12574
[30] High-order conforming finite elements for the Cahn–Hilliard equation: Relative-energy stability and energy defects
Submitted arXiv:2606.06719
[29] An Allen–Cahn equation with jump-diffusion noise for biological damage and repair processes
Submitted arXiv:2602.17495
[28] Unifying local and nonlocal corrosion frameworks: A convergent nonlocal extension of the KKS phase-field model
Submitted arXiv:2509.23503

Refereed articles

[9] 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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