• Corpus ID: 246016068

Theoretical and Practical Aspects of Space-Time DG-SEM Implementations

  title={Theoretical and Practical Aspects of Space-Time DG-SEM Implementations},
  author={Lea M. Versbach and Viktor Linders and Robert Kl{\"o}fkorn and Philipp Birken},
In this paper we discuss two approaches for the formulation and implementation of space-time discontinuous Galerkin spectral element methods (DG-SEM). In one, time is treated as an additional coordinate direction and a Galerkin procedure is applied to the entire problem. In the other, the method of lines is used with DG-SEM in space and the fully implicit Runge-Kutta method Lobatto IIIC in time. The two approaches are mathematically equivalent in the sense that they lead to the same discrete… 

Figures and Tables from this paper

Locally conservative and flux consistent iterative methods
Local conservation is established for all Krylov subspace methods, with and without restarts, and for Newton’s method under certain assumptions on the discretization, and it is shown that Newton-Krylov methods are locally conservative, although not necessarily flux consistent.


Unified form language: A domain-specific language for weak formulations of partial differential equations
The Unified Form Language is presented, which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation and generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations.
High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators
Dual-consistent GSBP time-marching methods are shown to retain: A and L-stability, as well as superconvergence of integral functionals when integrated with the quadrature associated with the discretization, which implies that the solution approximated at the end of each time step is superconversgent.
A generic interface for parallel and adaptive scientific computing: Abstraction principles and the Dune-Fem module
A general abstraction for a large class of grid-based discretization schemes for stationary and instationary partial differential equations by using modern template based generic programming techniques, including static polymorphism, the engine concept, and expression templates is derived.
Solving Ordinary Differential Equations II
Implementation of 3 stage Lobatto IIIC into Assimulo package
  • Bachelor thesis, Lund University
  • 2021
Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Methods
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 solving a wide
On an eigenvalue property of Summation-By-Parts operators
Three results pertaining to the eigenvalue property do not hold for all nullspace consistent SBP operators, and all pseudospectral methods satisfy the eIGenvalue property.
Python Bindings for the DUNE-FEM module
Local Fourier Analysis of a Space-Time Multigrid Method for DG-SEM for the Linear Advection Equation
A Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem and asymptotic convergence factors for the smoother and the two-grid method for both coarsening strategies are presented.
Numerical Methods for Unsteady Compressible Flow Problems