Time-Discrete Higher-Order ALE Formulations: Stability

Time-Discrete Higher-Order ALE Formulations: Stability

Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher order time stepping without space discretizat...

Time-discrete higher order ALE formulations: a priori error analysis

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds’ quadrature. They involve a mild restriction on the...

A Dg Approach to Higher Order Ale Formulations in Time

We review recent results [10, 9, 8] on time-discrete discontinuous Galerkin (dG) methods for advection-diffusion model problems defined on deformable domains and written on the Arbitrary Lagrangian Eulerian (ALE) framework. ALE formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. We desc...

Stability and Geometric Conservation Laws for Ale Formulations

Stability analysis of second-order time accurate schemes for ALE–FEM

In this work we will introduce and analyze the Arbitrary Lagrangian Eulerian formulation for a model problem of a scalar advection–diffusion equation defined on a moving domain. Moving from the results illustrated in our previous work [J. Num. Math. 7 (1999) 105], we will consider first and second-order time advancing schemes and analyze how the movement of the domain might affect accuracy and ...