First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
- 1 December 1994
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 31 (6) , 1785-1799
- https://doi.org/10.1137/0731091
Abstract
This paper develops ellipticity estimates and discretization error bounds for elliptic equations (with lower-order terms) that are reformulated as a least-squares problem for an equivalent first-order system. The main result is the proof of ellipticity, which is used in a companion paper to establish optimal convergence of multiplicative and additive solvers of the discrete systems.Keywords
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