Publications (30)
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…
Residual estimates for post-processors in elliptic problems
Andreas Dedner, Jan Giesselmann, Tristan Pryer +1
In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `twe…
The DUNE Framework: Basic Concepts and Recent Developments
Peter Bastian, Markus Blatt, Andreas Dedner +9
This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that hap…
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…
The Dune Python Module
Andreas Dedner, Martin Nolte
In this paper we present the new Dune-Python module which provides Python bindings for the Dune core, which is a C++ environment for solving partial differential equations. The aim…
A framework for implementing general virtual element spaces
Andreas Dedner, Alice Hodson
In this paper we present a framework for the construction and implementation of general virtual element spaces based on projections built from constrained least squares problems. B…
A surface finite element method for computational modelling of cell blebbing
Björn Stinner, Andreas Dedner, Adam Nixon
Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of b…
Adaptive discontinuous Galerkin methods on surfaces
Andreas Dedner, Pravin Madhavan
We present a dual weighted residual-based a posteriori error estimate for a discontinuous Galerkin (DG) approximation of a linear second-order elliptic problem on compact smooth co…
A posteriori analysis of fully discrete method of lines DG schemes for systems of conservation laws
Andreas Dedner, Jan Giesselmann
We present reliable a posteriori estimators for some fully discrete schemes applied to nonlinear systems of hyperbolic conservation laws in one space dimension with strictly convex…
Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio
Andreas Dedner, Eike Hermann Müller, Robert Scheichl
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical we…
Analysis of the discontinuous Galerkin method for elliptic problems on surfaces
Andreas Dedner, Pravin Madhavan, Björn Stinner
We extend the discontinuous Galerkin (DG) framework to a linear second-order elliptic problem on a compact smooth connected and oriented surface. An interior penalty (IP) method is…
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…
A two-layer approach for Coupling 1D/2D Shallow Water Flow Models
Andreas Dedner, Chinedu Nwaigwe
In this paper, we propose a novel approach for coupling 2D/1D shallow water flow models. Efficiently coupling these models is vital for simulating the flow and flooding of open cha…
Discontinuous Galerkin methods for hyperbolic and advection-dominated problems on surfaces
Andreas Dedner, Pravin Madhavan
We extend the discontinuous Galerkin (DG) framework to the analysis of first-order hyperbolic and advection-dominated problems posed on implicitly defined surfaces. The focus will…
The DUNE-ALUGrid Module
Martin Alkämper, Andreas Dedner, Robert Klöfkorn +1
In this paper we present the new DUNE-ALUGrid module. This module contains a major overhaul of the sources from the ALUgrid library and the binding to the DUNE software framework.…
High order discontinuous Galerkin methods on surfaces
Paola Antonietti, Andreas Dedner, Pravin Madhavan +3
We derive and analyze high order discontinuous Galerkin methods for second-order elliptic problems on implicitely defined surfaces in . This is done by carefully ad…
Convection in a Single Column -- Modelling, Algorithm and Analysis
Onno Bokhove, Bin Cheng, Andreas Dedner +5
The group focused on a model problem of idealised moist air convection in a single column of atmosphere. Height, temperature and moisture variables were chosen to simplify the math…
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…
On the stabilization of a virtual element method for an acoustic vibration problem
Linda Alzaben, Daniele Boffi, Andreas Dedner +1
In this paper we introduce an abstract setting for the convergence analysis of the virtual element approximation of an acoustic vibration problem. We discuss the effect of the stab…
Python Framework for HP Adaptive Discontinuous Galerkin Method for Two Phase Flow in Porous Media
Andreas Dedner, Birane Kane, Robert Klöfkorn +1
In this paper we present a framework for solving two phase flow problems in porous media. The discretization is based on a Discontinuous Galerkin method and includes local grid ada…
Isoparametric Virtual Element Methods
Andrea Cangiani, Andreas Dedner, Matthew Hubbard +1
We present two approaches to constructing isoparametric Virtual Element Methods of arbitrary order for linear elliptic partial differential equations on general two-dimensional dom…
Formulation, Implementation and Validation of the Horizontal Coupling Method for 1D/2D Shallow Water Flow Models
Chinedu Nwaigwe, Andreas Dedner
One dimensional (1D) simulations of the flow and flooding of open channels are known to be inaccurate as the flow is multi-dimensional in nature, especially at the flooded regions.…
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…
Convergence Properties of Iteratively Coupled Surface-Subsurface Models
Valentina Schüller, Philipp Birken, Andreas Dedner
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A…
DDFEM: A Python Package for Diffuse Domain Methods
Luke Benfield, Andreas Dedner
Solving partial differential equations (PDEs) on complex domains can present significant computational challenges. The Diffuse Domain Method (DDM) is an alternative that reformulat…
Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method
Andreas Dedner, Robert Klöfkorn
This paper discusses a Python interface for the recently published DUNE-FEM-DG module which provides highly efficient implementations of the Discontinuous Galerkin (DG) method for…
Discontinuous Galerkin methods for nonvariational problems
Andreas Dedner, Tristan Pryer
We extend the finite element method introduced by Lakkis and Pryer [2011] to approximate the solution of second order elliptic problems in nonvariational form to incorporate the di…
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…
Robust nonconforming virtual element methods for general fourth order problems with varying coefficients
Andreas Dedner, Alice Hodson
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructin…
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…