Dr. Marvin Fritz

Numerical Analysis of PDEs, Mathematical Modeling & Computational Science

Publications

For a complete list of my work, including preprints and citations, see my profiles on arXiv, ResearchGate, Google Scholar, ORCID.

Preprints

  1. Unifying local and nonlocal corrosion frameworks: A convergent nonlocal extension of the KKS phase-field model
    with C. Cyron, A. Hermann, T. Köppl, A. Shojaei, S. Silling
    Mathematical Models and Methods in Applied Sciences (submitted)
    Links: Preprint
  2. Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility
    with A. Brunk
    Partial Differential Equations and Applications (submitted)
    Links: Preprint

Peer-Reviewed Scientific Articles

  1. On feedback stabilisation for the Cahn-Hilliard equation and its numerical approximation
    with H. Egger, K. Kunisch, S. Rodrigues
    IMA Journal of Numerical Analysis (2025)
    Links: Preprint & Journal
  2. Analysis and structure-preserving approximation of a Cahn-Hilliard-Forchheimer system with solution-dependent mass and volume source
    with A. Brunk
    ESAIM: Mathematical Modelling and Numerical Analysis (2025)
    Links: Preprint & Journal
  3. Stabilization to trajectories of nonisothermal Cahn-Hilliard equations
    with B. Azmi and S. Rodrigues
    ESAIM: Control, Optimisation and Calculus of Variations (2025)
    Links: Preprint & Journal
  4. Well-posedness, long-time behavior, and discretization of some models of nonlinear acoustics in velocity-enthalpy formulation
    with H. Egger
    Mathematical Methods in the Applied Sciences (2025)
    Links: Preprint & Journal
  5. Analysis and computations of a stochastic Cahn-Hilliard model for tumor growth with chemotaxis and variable mobility
    with L. Scarpa
    Stochastics and Partial Differential Equations: Analysis and Computations (2025)
    Links: Preprint & Journal
  6. Structure-preserving approximation of the Cahn-Hilliard-Biot system
    with A. Brunk
    Numerical Methods for Partial Differential Equations (2025)
    Links: Preprint & Journal
  7. On the well-posedness of the Cahn-Hilliard-Biot model and its applications to tumor growth
    Discrete and Continuous Dynamical Systems - S (2024)
    Links: Preprint & Journal
  8. Well-posedness and simulation of weak solutions to the time-fractional Fokker-Planck equation with general forcing
    Discrete and Continuous Dynamical Systems - B (2024)
    Links: Preprint & Journal
  9. Analysis of a dilute polymer model with a time-fractional derivative
    with E. Süli and B. Wohlmuth
    SIAM Journal on Mathematical Analysis (2024)
    Links: Preprint & Journal
  10. A phase-field model for non-small cell lung cancer under the effects of immunotherapy
    with C. Kuttler, J.T. Oden, P. Schlicke, C. Schumann, A. Wagner and B. Wohlmuth
    Mathematical Biosciences and Engineering (2023)
    Links: Preprint & Journal
  11. Tumor evolution models of phase-field type with nonlocal effects and angiogenesis
    Bulletin of Mathematical Biology (2023)
    Links: Preprint & Journal
  12. Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
    with U. Khristenko and B. Wohlmuth
    Advances in Nonlinear Analysis (2023)
    Links: Preprint & Journal
  13. A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue
    with T. Köppl, J.T. Oden, A. Wagner, B. Wohlmuth and C. Wu
    International Journal for Numerical Methods in Biomedical Engineering (2022)
    Links: Preprint & Journal
  14. Time-fractional Cahn-Hilliard equation: Well-posedness, degeneracy, and numerical solutions
    with M.L. Rajendran and B. Wohlmuth
    Computers & Mathematics with Applications (2022)
    Links: Preprint & Journal
  15. On a subdiffusive tumour growth model with fractional time derivative
    with C. Kuttler, M.L. Rajendran, L. Scarabosio and B. Wohlmuth
    IMA Journal of Applied Mathematics (2021)
    Links: Preprint & Journal
  16. Modeling and simulation of vascular tumors embedded in evolving capillary networks
    with P.K. Jha, T. Köppl, J.T. Oden, A. Wagner and B. Wohlmuth
    Computer Methods in Applied Mechanics and Engineering (2021)
    Links: Preprint & Journal
  17. Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network
    with P.K. Jha, T. Köppl, J.T. Oden, B. Wohlmuth
    Nonlinear Analysis: Real World Applications (2020)
    Links: Preprint & Journal
  18. Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation
    with E.A.B.F. Lima, V. Nikolić, J.T. Oden and B. Wohlmuth
    Mathematical Models and Methods in Applied Sciences (2019)
    Links: Preprint & Journal
  19. On the unsteady Darcy-Forchheimer-Brinkman equation in local and nonlocal tumor growth models
    with E.A.B.F. Lima, J.T. Oden and B. Wohlmuth
    Mathematical Models and Methods in Applied Sciences (2019)
    Links: Preprint & Journal
  20. Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics
    with V. Nikolić and B. Wohlmuth
    Mathematical Models and Methods in Applied Sciences (2018)
    Links: Preprint & Journal
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    Theses

    1. Well-posedness of nonlocal and mixed-dimensional phase-field models applied to tumor growth
      PhD Dissertation, Technical University of Munich (2022)
      Supervisor: Prof. Dr. Barbara Wohlmuth
      Links: MediaTUM
    2. The recent existence proofs of the Navier-Stokes equations
      Master's Thesis, Technical University of Munich (2017)
      Supervisor: Prof. Dr. Hans Wilhelm Alt

    3. On the stability of relative equilibria in vortex dynamics
      Bachelor's Thesis, Technical University of Munich (2015)
      Supervisor: Prof. Dr. Jürgen Scheurle