Hybrid First-Order System Least Squares Finite Element Methods with Application to Stokes Equations
| Autor: | Lei Tang, Kuo Liu, Thomas A. Manteuffel, John W. Ruge, Stephen F. McCormick |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | SIAM Journal on Numerical Analysis. 51:2214-2237 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/120868906 |
| Popis: | This paper combines first-order system least squares (FOSLS) with first-order system $LL^*$ (FOSLL$^*$) to create a Hybrid method. The FOSLS approach minimizes the error, ${\bf e}^h = {\bf u}^h - {\bf u}$, over a finite element subspace, ${\cal V}^h$, in the operator norm: $\min_{{\bf u}^h\in{\cal V}^h}\| L ({\bf u}^h-{\bf u})\|$. The FOSLL$^*$ method looks for an approximation in the range of $L^*$, setting ${\bf u}^h = L^*{\bf w}^h$ and choosing ${\bf w}^h \in {\cal W}^h$, a standard finite element space. FOSLL$^*$ minimizes the $L^2$ norm of the error over $L^*({\cal W}^h)$: $\min_{{\bf w}^h\in{\cal W}^h} \| L^*{\bf w}^h - {\bf u}\|$. FOSLS enjoys a locally sharp, globally reliable, and easily computable a posteriori error estimate, while FOSLL$^*$ does not. However, FOSLL$^*$ has the major advantage that it applies to problems that do not exhibit enough smoothness to enable the full advantages that the FOSLS approach otherwise provides. The Hybrid method attempts to retain the best properties of both ... |
| Databáze: | OpenAIRE |
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