کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8902660 1632146 2018 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Diagonalized Legendre spectral methods using Sobolev orthogonal polynomials for elliptic boundary value problems
ترجمه فارسی عنوان
روش طیفی افقی افقی افقی با استفاده از چندجمله ای متعامد سوبووال برای مشکلات مرزی بیضوی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
چکیده انگلیسی
Fully diagonalized spectral methods using Sobolev orthogonal/biorthogonal basis functions are proposed for solving second order elliptic boundary value problems. We first construct the Fourier-like Sobolev polynomials which are mutually orthogonal (resp. bi-orthogonal) with respect to the bilinear form of the symmetric (resp. unsymmetric) elliptic Neumann boundary value problems. The exact and approximation solutions are then expanded in an infinite and truncated series in the Sobolev orthogonal polynomials, respectively. An identity is also established for the a posterior error estimate with a simple error indicator. Further, the Fourier-like Sobolev orthogonal polynomials and the corresponding Legendre spectral method are proposed in parallel for Dirichlet boundary value problems. Numerical experiments illustrate that our Legendre methods proposed are not only efficient for solving elliptic problems but also equally applicable to indefinite Helmholtz equations and singular perturbation problems.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 127, May 2018, Pages 196-210
نویسندگان
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