# High Order ADER Schemes for Continuum Mechanics

@inproceedings{Busto2020HighOA, title={High Order ADER Schemes for Continuum Mechanics}, author={S. Busto and Simone Chiocchetti and Michael Dumbser and Elena Gaburro and Ilya Peshkov}, booktitle={Frontiers in Physics}, year={2020} }

In this paper we first review the development of high order ADER finite volume and ADER discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in 1999 by Toro et al. We show the modern variant of ADER based on a space-time predictor-corrector formulation in the context of ADER discontinuous Galerkin schemes with a posteriori subcell finite volume limiter on fixed and moving grids, as well as on space-time adaptive Cartesian AMR meshes. We then present and discuss… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Citations

##### Publications citing this paper.

SHOWING 1-5 OF 5 CITATIONS

## Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure

VIEW 6 EXCERPTS

CITES BACKGROUND & METHODS

## A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies

VIEW 2 EXCERPTS

CITES METHODS & BACKGROUND

## High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension

VIEW 2 EXCERPTS

CITES BACKGROUND & METHODS

## A new continuum model for general relativistic viscous heat-conducting media

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 193 REFERENCES

## An efficient high order direct ALE ADER finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## On the eigenvalues of the ADER-WENO Galerkin predictor

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL