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Interpolation by various types of splines is the standard procedure in manyapplications. In this paper we shall discuss harmonic spline "interpolation"(on the lines of a grid) as an alternative to polynomial spline interpolation(at vertices of a grid). We will discuss some advantages and drawbacks of thisapproach and present the asymptotics of the $L_p$-error for adaptiveapproximation by harmonic splines.

On the $L_p$-error of approximation of bivariate functions by harmonic splines