Least squares methods for $2m$th order elliptic boundary-value problems

Least Squares for Second Order Elliptic Problems

In this paper we introduce and analyze two least squares methods for second order elliptic di erential equations with mixed boundary conditions These methods extend to problems which involve oblique derivative boundary conditions as well as nonsym metric and inde nite problems as long as the original problem has a unique solution With the methods to be developed Neumann and oblique boundary con...

Wavelet Least Squares Methods for Boundary Value Problems

The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem

In [Z. Cai, T. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 34 (1997), pp. 425–454], an L2-norm version of first-order system least squares (FOSLS) was developed for scalar second-order elliptic partial differential equations. A limitation of this approach is the requirement of sufficient smoothness of the original problem, which is used for the equivalence of spaces between (H1)d and...

Least-squares Finite Element Methods for First-order Elliptic Systems

Least-squares principles use artificial " energy " functionals to provide a Rayleigh-Ritz-like setting for the finite element method. These function-als are defined in terms of PDE's residuals and are not unique. We show that viable methods result from reconciliation of a mathematical setting dictated by the norm-equivalence of least-squares functionals with practicality constraints dictated by...

Semidiscrete-Least Squares Methods for a Parabolic Boundary Value Problem

In this paper some approximate methods for solving the initial-boundary value problem for the heat equation in a cylinder under homogeneous boundary conditions are analyzed. The methods consist in discretizing with respect to time and solving approximately the resulting elliptic problem for fixed time by least squares methods. The approximate solutions will belong to a finite-dimensional subspa...