6 papers
Virtual element methods for a class of fully nonlinear elliptic PDEs
Guillaume Bonnet, Andrea Cangiani, Andreas Dedner +1
We study virtual element discretizations of a well-known variational formulation in of Hamilton-Jacobi-Bellman and Isaacs equations with Cordes coefficients. We show that the…
Diffuse Domain Methods with Dirichlet Boundary Conditions
Luke Benfield, Andreas Dedner
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diff…
A posteriori analysis for nonlinear convection-diffusion systems
Andreas Dedner, Jan Giesselmann, Kiwoong Kwon +1
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we…
Bryne: sustainable prototyping of finite element models
Benjamin Terschanski, Robert Klöfkorn, Andreas Dedner +1
Open-source simulation frameworks are evolving rapidly to provide accessible tools for the numerical solution of partial differential equations. Modern finite element (FEM) softwar…
The Distributed and Unified Numerics Environment (DUNE), Version 2.10
Markus Blatt, Samuel Burbulla, Ansgar Burchardt +9
Version 2.10 of the Distributed and Unified Numerics Environment DUNE introduces a range of enhancements across its core and extension modules, with a continued emphasis on modern…
Jacobian-free Multigrid Preconditioner for Discontinuous Galerkin Methods applied to Numerical Weather Prediction
Philipp Birken, Andreas Dedner, Robert Klöfkorn
Discontinuous Galerkin (DG) methods are promising high order discretizations for unsteady compressible flows. Here, we focus on Numerical Weather Prediction (NWP). These flows are…