Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG)
finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic …
finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic …
An optimization-based framework for anisotropic simplex mesh adaptation
M Yano, DL Darmofal - Journal of Computational Physics, 2012 - Elsevier
We present a general framework for anisotropic h-adaptation of simplex meshes. Given a
discretization and any element-wise, localizable error estimate, our adaptive method iterates …
discretization and any element-wise, localizable error estimate, our adaptive method iterates …
Error estimation and adaptive mesh refinement for aerodynamic flows
R Hartmann, J Held, T Leicht, F Prill - … by the European Union, 2006-2009, 2010 - Springer
We consider the adjoint-based error estimation and goal-oriented mesh refinement for
single and multiple aerodynamic force coefficients as well as residual-based mesh …
single and multiple aerodynamic force coefficients as well as residual-based mesh …
Semi-implicit discontinuous Galerkin methods for the incompressible Navier–Stokes equations on adaptive staggered Cartesian grids
In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is
presented for the solution of the incompressible Navier–Stokes equations on staggered …
presented for the solution of the incompressible Navier–Stokes equations on staggered …
An efficient and accurate implicit DG solver for the incompressible Navier–Stokes equations
G Orlando, A Della Rocca, PF Barbante… - … Methods in Fluids, 2022 - Wiley Online Library
We propose an efficient, accurate, and robust implicit solver for the incompressible Navier–
Stokes equations, based on a DG spatial discretization and on the TR‐BDF2 method for time …
Stokes equations, based on a DG spatial discretization and on the TR‐BDF2 method for time …
A goal-oriented high-order anisotropic mesh adaptation using discontinuous Galerkin method for linear convection-diffusion-reaction problems
We deal with the numerical solution of a linear convection-diffusion-reaction equation using
the discontinuous Galerkin method of arbitrary polynomial approximation degree on …
the discontinuous Galerkin method of arbitrary polynomial approximation degree on …
Anisotropic a posteriori error estimate for the virtual element method
PF Antonietti, S Berrone, A Borio… - IMA Journal of …, 2022 - academic.oup.com
We derive an anisotropic a posteriori error estimate for the adaptive conforming virtual
element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we …
element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we …
Discontinuous Galerkin methods for compressible and incompressible flows on space–time adaptive meshes: toward a novel family of efficient numerical methods for …
F Fambri - Archives of Computational Methods in Engineering, 2020 - Springer
In this work the numerical discretization of the partial differential governing equations for
compressible and incompressible flows is dealt within the discontinuous Galerkin (DG) …
compressible and incompressible flows is dealt within the discontinuous Galerkin (DG) …
hp-DGFEM for nonlinear convection-diffusion problems
V Dolejší - Mathematics and Computers in Simulation, 2013 - Elsevier
We deal with a numerical solution of nonlinear convection-diffusion problems with the aid of
the discontinuous Galerkin finite element method (DGFEM). We propose a new hp …
the discontinuous Galerkin finite element method (DGFEM). We propose a new hp …
Automatic symbolic computation for discontinuous Galerkin finite element methods
The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents
a very challenging computational task, particularly for systems of coupled nonlinear PDEs …
a very challenging computational task, particularly for systems of coupled nonlinear PDEs …