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• W3000402387 abstract "We prove an optimal-order error bound in the discrete $H^2(Omega)$ norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in $n$ space dimensions, with $n in {2,dots,7}$, whose generalized solution belongs to the Sobolev space $H^s(Omega) cap H^2_0(Omega)$ for $frac{1}{2} max(5,n) < s leq 4$, where $Omega = (0,1)^n$. The result extends the range of the Sobolev index $s$ in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of $H^s(Omega)$ into $C(overlineOmega)$ in $n$ space dimensions." @default.
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• W3000402387 date "2020-01-01" @default.
• W3000402387 modified "2023-10-15" @default.
• W3000402387 title "Optimal-Order Finite Difference Approximation of Generalized Solutions to the Biharmonic Equation in a Cube" @default.
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• W3000402387 doi "https://doi.org/10.1137/19m1254313" @default.
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