6 papers
Rothe time discretization and weak solutions for a cutoff Westervelt system
Marvin Fritz
We study a fully implicit Rothe time discretization for a cutoff first-order formulation of the Westervelt equation. The key ingredients are the enthalpy variable and the primitive…
A fractional de Rham complex for coframe-attached Maxwell equations
Marvin Fritz
We develop a coordinate-anchored pointwise theory of fractional tangent functionals on bounded rectangles. By working on the range of the coordinatewise Riemann-Liouville integral,…
High-order conforming finite elements for the Cahn-Hilliard equation: Relative-energy stability and energy defects
Aaron Brunk, Marvin Fritz
We study a semidiscrete single-field Galerkin approximation of the Cahn-Hilliard equation using high-order conforming finite element spaces. More specifically, globally finit…
On feedback stabilisation for the Cahn-Hilliard equation and its numerical approximation
Herbert Egger, Marvin Fritz, Karl Kunisch +1
We consider the stabilisation of solutions to the Cahn-Hilliard equation towards a given trajectory by means of a finite-dimensional static output feedback mechanism. Exponential s…
Stabilization to trajectories of nonisothermal Cahn-Hilliard equations
Behzad Azmi, Marvin Fritz, Sérgio S. Rodrigues
In this work, it is proven the semiglobal exponential stabilization to time-dependent trajectories of the nonisothermal Cahn-Hilliard equations. In the model, the input controls ar…
Well-posedness, long-time behavior, and discretization of some models of nonlinear acoustics in velocity-enthalpy formulation
Herbert Egger, Marvin Fritz
We study a class of models for nonlinear acoustics, including the well-known Westervelt and Kuznetsov equations, as well as a model of Rasmussen that can be seen as a thermodynamic…