A note on the conservation properties of the generalized-$\alpha$ method
Numerical Analysis
2022-02-10 v1 Numerical Analysis
Abstract
We show that the second-order accurate generalized- method on a uniform temporal mesh may be viewed as an implicit midpoint method on a shifted temporal mesh. With this insight, we demonstrate generalized- time integration of a finite element spatial discretization of a conservation law system results in a fully-discrete method admitting discrete balance laws when (i) the time integration is second-order accurate, (ii) a uniform temporal mesh is employed, (iii) the spatial discretization is conservative, and (iv) conservation variables are discretized.
Cite
@article{arxiv.2202.04568,
title = {A note on the conservation properties of the generalized-$\alpha$ method},
author = {DeAnna S. Gilchrist and John A. Evans},
journal= {arXiv preprint arXiv:2202.04568},
year = {2022}
}