The Runge–Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws
In this paper, we present a novel class of high-order Runge–Kutta (RK) discontinuous
Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond …
Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond …
Space–time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional …
IS Popov - Computers & Fluids, 2024 - Elsevier
The space–time adaptive ADER–DG finite element method with LST–DG predictor and a
posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of …
posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of …
[HTML][HTML] Eigensolution analysis of immersed boundary method based on volume penalization: applications to high-order schemes
J Kou, A Hurtado-de-Mendoza, S Joshi… - Journal of …, 2022 - Elsevier
This paper presents eigensolution and non-modal analyses for immersed boundary
methods (IBMs) based on volume penalization for the linear advection equation. This …
methods (IBMs) based on volume penalization for the linear advection equation. This …
A robust CFL condition for the discontinuous Galerkin method on triangular meshes
When the discontinuous Galerkin (DG) method is applied to hyperbolic problems in two
dimensions on triangular meshes and paired with an explicit time integration scheme, an …
dimensions on triangular meshes and paired with an explicit time integration scheme, an …
Space-Time Adaptive ADER-DG Finite Element Method with LST-DG Predictor and a posteriori Sub-cell WENO Finite-Volume Limiting for Simulation of Non …
IS Popov - Journal of Scientific Computing, 2023 - Springer
The space-time adaptive ADER finite element DG method with a posteriori correction
technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to …
technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to …
An analysis of the spectrum of the discontinuous Galerkin method
L Krivodonova, R Qin - Applied Numerical Mathematics, 2013 - Elsevier
We derive explicit expressions for the eigenvalues (spectrum) of the discontinuous Galerkin
spatial discretization applied to the linear advection equation. We show that the eigenvalues …
spatial discretization applied to the linear advection equation. We show that the eigenvalues …
Operator bounds and time step conditions for the DG and central DG methods
Discontinuous Galerkin (DG) and central DG methods are two related families of finite
element methods. They can provide high order spatial discretizations that are often …
element methods. They can provide high order spatial discretizations that are often …
The effective use of BLAS interface for implementation of finite-element ADER-DG and finite-volume ADER-WENO methods
IS Popov - arxiv preprint arxiv:2409.12483, 2024 - arxiv.org
Numerical methods of the ADER family, in particular finite-element ADER-DG and finite-
volume ADER-WENO methods, are among the most accurate numerical methods for solving …
volume ADER-WENO methods, are among the most accurate numerical methods for solving …
Discontinuous Galerkin Spectral Element Methods for Astrophysical Flows in Multi-physics Applications
J Markert - 2022 - elib.dlr.de
In engineering applications, discontinuous Galerkin methods (DG) have been proven to be a
powerful and flexible class of high order methods for problems in computational fluid …
powerful and flexible class of high order methods for problems in computational fluid …
Comparative Fourier analysis of DG, FD and compact difference schemes
In this paper, we compare the semi-discrete behavior of several numerical methods
including the Discontinuous Galerkin (DG), classical Finite Difference (FD), Dispersion …
including the Discontinuous Galerkin (DG), classical Finite Difference (FD), Dispersion …