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- W1992204554 abstract "In this note we consider semidiscrete and multistep fully discrete Galerkin approximations (in the space of smooth periodic splines $S^mu ,mu geqq 2$, on a uniform mesh with mesh length h) to the solution of the initial-periodic boundary value problem for a second-order hyperbolic equation with space-varying coefficients. We show that a suitable choice of the initial conditions for the Galerkin equations leads to increased accuracy (superconvergence) of the approximate solution which is $O(h^{2mu - 2} )$-accurate when compared with a certain quasiinterpolant of the exact solution. We also analyze the effect of numerical integration on the superconvergence of the error estimates. We present the results of numerical experiments with cubic splines in one dimension and bicubic splines on squares coupled with the Størmer-Numerov time-differencing method." @default.
- W1992204554 created "2016-06-24" @default.
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- W1992204554 date "1980-06-01" @default.
- W1992204554 modified "2023-10-17" @default.
- W1992204554 title "On the Superconvergence of Galerkin Approximations to Second-Order Hyperbolic Equations" @default.
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- W1992204554 doi "https://doi.org/10.1137/0717037" @default.
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