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Convergence studies of least-squares finite elements for first-order systems. (English) Zbl 0684.65083

A least-squares finite element method for first order systems describing two-point boundary value problems is constructed. Comparison studies are made with the corresponding mixed Galerkin formulation for the same system. Some heuristic results are obtained, to the effect that the least-squares method has superior convergence properties than the mixed method. Some superconvergence properties of the least-squares method are identified.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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