Adaptive finite element methods for the analysis of inviscid compressible flow: I: Fast refinement/unrefinement and moving mesh methods for unstructured meshes. (English) Zbl 0593.76080

New adaptive finite element methods are presented for the analysis of unsteady inviscid compressible flow in arbitrary two-dimensional domains. The procedures described herein are used in conjunction with a semi- explicit two-step algorithm for solving the time-dependent Euler equations in two space dimensions. Two schemes are presented for monitoring the evolution of error, and error estimates are used as a basis for a mesh refinement strategy. The capability of unrefinement (adaptively coarsening the mesh) is also included. The methods do not require a structured mesh and are applicable to quite general geometries.


76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M99 Basic methods in fluid mechanics
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