5 papers · 1 filter
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…
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…
A higher order nonconforming virtual element method for the Cahn-Hilliard equation
Andreas Dedner, Alice Hodson
In this paper we develop a fully nonconforming virtual element method (VEM) of arbitrary approximation order for the two dimensional Cahn-Hilliard equation. We carry out the error…