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- W3164962444 abstract "Assume that $ S_0 Psi = g $ is the one-dimensional form of modified Symm's integral equation of the first kind on bounded and simply connected domain of $ C^3 $ class. $ S_0 $ can be seen as an operator mapping from $ L^2(0,2pi) $ to itself. Following the techniques in [1, Chapter 3] and [12], we establish the convergence and error analysis in $ L^2 $ setting for Petrov-Galerkin methods under Fourier basis when $ g in H^r(0,2pi), r geq 1 $, and prove that the optimal convergence rate are obtained for least squares and Bubnov-Galerkin methods. Besides, we prove that, when $ g in H^r(0,2pi), 0 leq r < 1 $, the least squares, dual least squares, Bubnov-Galerkin methods with Fourier basis will uniformly diverge to infinity at optimal first order. As a supplementary result to above divergence, we show the convergence in $ H^{-1} $ and $ H^{-frac{1}{2}} $ for dual least squares, Bubnov-Galerkin methods when $ g in H^r(0,2pi), 0 leq r < 1 $ and $ g in H^r(0,2pi), frac{1}{2} leq r < 1 $ respectively." @default.
- W3164962444 created "2021-06-07" @default.
- W3164962444 creator A5007883911 @default.
- W3164962444 date "2020-03-28" @default.
- W3164962444 modified "2023-09-27" @default.
- W3164962444 title "Petrov-Galerkin methods with Fourier basis on modified Symm's integral equation of the first kind" @default.
- W3164962444 hasPublicationYear "2020" @default.
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