Euler Calculations by Upwind Finite Element Methods and Adaptive Mesh Algorithms

Abstract

Thia paper presents Euler calculations employing several recent developments:
- a family of upwind finite-element schemes based on approximate Riemann solvers,
- mesh adaption procedures.
The approximation is a second-order accurate MUSCL-like scheme, that includes monotonicity-preserving limiters. Efficiency is achieved by an implicit formulation. The solution procedure is combined with a mesh enrichment algorithm
by local element division, and a node movement algorithmmore specifically adapted to accurately capture 1-D structures (shocks, layers...).