کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645360 | 1632209 | 2013 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An analysis of the spectrum of the discontinuous Galerkin method
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: An analysis of the spectrum of the discontinuous Galerkin method An analysis of the spectrum of the discontinuous Galerkin method](/preview/png/4645360.png)
چکیده انگلیسی
We derive explicit expressions for the eigenvalues (spectrum) of the discontinuous Galerkin spatial discretization applied to the linear advection equation. We show that the eigenvalues are related to the subdiagonal [p/p+1] Padé approximation of exp(−z) when pth degree basis functions are used. We derive an upper bound on the eigenvalue with the largest magnitude as (p+1)(p+2). We demonstrate that this bound is not tight and prove that the asymptotic growth rate of the spectral radius is slower than quadratic in p. We also analyze the behavior of the spectrum near the imaginary axis to demonstrate that the spectral curves approach the imaginary axis although there are no purely imaginary eigenvalues.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 64, February 2013, Pages 1-18
Journal: Applied Numerical Mathematics - Volume 64, February 2013, Pages 1-18