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Dynamic refinement algorithms for spectral element methods. (English) Zbl 0927.76077

Summary: A numerical method is presented that combines high-order domain decomposition and adaptive mesh refinement. The spatial discretization is based on a nonconforming spectral element method. Meshes are generated by adaptive refinement of a quadtree using either local solution gradients or the local polynomial spectrum as refinement criteria. The method is applied to solve scalar test problems and to simulate the flow in a lid-driven cavity at moderate Reynolds numbers.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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