First-order system least squares for second-order partial differential equations: Part I Academic Article uri icon

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.

author list (cited authors)

  • Cai, Z., Lazarov, R., Manteuffel, T. A., & McCormick, S. F.

citation count

  • 236

publication date

  • January 1994