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This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.
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참고문헌 (26)
참고문헌 신청
A. I. Pehlivanov / 1994 / Least-squares mixed finite elements for second-order elliptic problems / SIAM J. Numer. Anal 31 (5) : 1368 ~ 1377
A. K. Aziz / 1985 / Least squares methods for elliptic systems / Math. Comp 44 (169) : 53 ~ 70
A. Loubenets / 2009 / Highly accurate finite element method for one- dimensional elliptic interface problems / Appl. Numer. Math 59 (1) : 119 ~ 134
A. Quarteroni / 1994 / Numerical Approximation of Partial Differ
B.-N. Jiang / 1998 / The Least-Squares Finite Element Method / Springer-Verlag
A. K. Aziz / 1985 / Least squares methods for elliptic systems / Math. Comp 44 (169) : 53 ~ 70
A. Loubenets / 2009 / Highly accurate finite element method for one- dimensional elliptic interface problems / Appl. Numer. Math 59 (1) : 119 ~ 134
A. Quarteroni / 1994 / Numerical Approximation of Partial Differ
B.-N. Jiang / 1998 / The Least-Squares Finite Element Method / Springer-Verlag
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