S. Franz

activity

20192021

collaborators

4 papers

math.NA2021

Singularly perturbed reaction-diffusion problems as first order systems

Sebastian Franz

We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{d i v}$ -co…

math.NA2021

Anisotropic $H_{d i v}$ -norm error estimates for rectangular $H_{d i v}$ -elements

Sebastian Franz

For the discretisation of $H_{d i v}$ -functions on rectangular meshes there are at least three families of elements, namely Raviart-Thomas-, Brezzi-Douglas-Marini- and Arnold-Boffi-F…

math.NA2020

Mixed $h p$ FEM for singularly perturbed fourth order boundary value problems with two small parameters

C. Xenophontos, S. Franz, I. Sykopetritou

We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $h p$ version of the Finite Element M…

math.NA2019

Continuous time integration for changing type systems

Sebastian Franz

We consider variational time integration using continuous Galerkin Petrov methods applied to evolutionary systems of changing type. We prove optimal-order convergence of the error…

Singularly perturbed reaction-diffusion problems as first order systems

Anisotropic Hdiv​-norm error estimates for rectangular Hdiv​-elements

Mixed hp FEM for singularly perturbed fourth order boundary value problems with two small parameters

Continuous time integration for changing type systems

Anisotropic $H_{d i v}$ -norm error estimates for rectangular $H_{d i v}$ -elements

Mixed $h p$ FEM for singularly perturbed fourth order boundary value problems with two small parameters