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Superconsistent discretizations. (English) Zbl 0999.65073
Summary: We say that the approximation of a linear operator is superconsistent when the exact and the discrete operators coincide on a functional space whose dimension is bigger than the number of degrees of freedom needed in the construction of the discretization. By providing several examples, we show how to build up superconsistent schemes. Many open questions will be also rised and partially discussed.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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