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Regularity and convergence analysis in Sobolev and Hölder spaces for generalized Whittle–Matérn fields

2020
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Numerische Mathematik
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AbstractWe analyze several types of Galerkin approximations of a Gaussian random field $$\mathscr {Z}:\mathscr {D}\times \varOmega \rightarrow \mathbb {R}$$ Z : D × Ω → R indexed by a Euclidean domain $$\mathscr {D}\subset \mathbb {R}^d$$ D ⊂ R d whose covariance structure is determined by a negative fractional power $$L^{-2\beta }$$ L - 2 β of a second-order elliptic differential operator $$L:= -\nabla \cdot (A\nabla ) + \kappa ^2$$ L : = - ∇ · ( A ∇ ) + κ 2 . Under minimal assumptions on the

doi:10.1007/s00211-020-01151-x
fatcat:ihfke4espjgoplrl4wcscsyzzy