6 papers
Well-posedness and time stepping adaptivity for a class of collocation discretisations of time-fractional subdiffusion equations
Sebastian Franz, Natalia Kopteva
Time-fractional parabolic equations with a Caputo time derivative of order are discretised in time using collocation methods, which assume that the Caputo derivative of…
Numerical Treatment of Non-local Integral Operators in the Framework of Evolutionary Equations
Sebastian Franz, Sascha Trostorff
Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness o…
On the solution existence for collocation discretizations of time-fractional subdiffusion equations
Sebastian Franz, Natalia Kopteva
Time-fractional parabolic equations with a Caputo time derivative of order are discretized in time using continuous collocation methods. For such discretizations, we gi…
Time stepping adaptation for subdiffusion problems with non-smooth right-hand sides
Sebastian Franz, Natalia Kopteva
We consider a time-fractional subdiffusion equation with a Caputo derivative in time, a general second-order elliptic spatial operator, and a right-hand side that is non-smooth in…
Structure preserving discontinuous Galerkin approximation of a hyperbolic-parabolic system
Markus Bause, Sebastian Franz
We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin space-time finite element methods. The model is rewritten as a f…
Numerical analysis of a singularly perturbed 4th order problem with a shift term
Sebastian Franz, Kleio Liotati
We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner laye…