A priori and a posteriori error analysis for a large-scale ocean circulation finite element model
| Autor: | J. M. Cascón, Galina C. García, Rodolfo Rodríguez |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Hessian matrix
Mathematical optimization Scale (ratio) Mechanical Engineering Computational Mechanics General Physics and Astronomy Finite element method Computer Science Applications symbols.namesake Rate of convergence Mechanics of Materials Stream function symbols Applied mathematics A priori and a posteriori Polygon mesh Uniqueness Mathematics |
| Zdroj: | Computer Methods in Applied Mechanics and Engineering. 192:5305-5327 |
| ISSN: | 0045-7825 |
| DOI: | 10.1016/j.cma.2003.09.002 |
| Popis: | We consider the finite element solution of the stream function–vorticity formulation for a large-scale ocean circulation model. First, we study existence and uniqueness of solution for the continuous and discrete problems. Under appropriate regularity assumptions we prove that the stream function can be computed with an error of order h in H1-seminorm. Second, we introduce and analyze an h-adaptive mesh refinement strategy to reduce the spurious oscillations and poor resolution which arise when convective terms are dominant. We propose an a posteriori anisotropic error indicator based on the recovery of the Hessian from the finite element solution, which allows us to obtain well adapted meshes. The numerical experiments show an optimal order of convergence of the adaptive scheme. Furthermore, this strategy is efficient to eliminate the oscillations around the boundary layer. |
| Databáze: | OpenAIRE |
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