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In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.
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참고문헌 (27)
참고문헌 신청
P. B. Bochev / 1998 / Finite element methods of least-squares type / SIAM Review 40:789~837
J.H. Bramble / 1997 / A least-squares approach based on a discrete minus one inner product for first order systems / Math. Comp 66(219):935~955
C. Bernardi / 1992 / Approximation Spectrales de Problemes aux Limites Elliptiques / Springer-Verlag
J. H. Bramble / 1998 / A negative-norm least squares method for Reissner-Mindlin plates / Math. Comp. 67:901~916
Z. Cai / 1994 / First-order system least squares for second-order partial differential equations: Part I / SIAM J. Numer. Anal. 31:1785~1799
J.H. Bramble / 1997 / A least-squares approach based on a discrete minus one inner product for first order systems / Math. Comp 66(219):935~955
C. Bernardi / 1992 / Approximation Spectrales de Problemes aux Limites Elliptiques / Springer-Verlag
J. H. Bramble / 1998 / A negative-norm least squares method for Reissner-Mindlin plates / Math. Comp. 67:901~916
Z. Cai / 1994 / First-order system least squares for second-order partial differential equations: Part I / SIAM J. Numer. Anal. 31:1785~1799
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