کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8902551 | 1632141 | 2018 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The lumped mass FEM for a time-fractional cable equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We consider the numerical approximation of a time-fractional cable equation involving two Riemann-Liouville fractional derivatives. We investigate a semidiscrete scheme based on the lumped mass Galerkin finite element method (FEM), using piecewise linear functions. We establish optimal error estimates for smooth and middly smooth initial data, i.e., vâHq(Ω)â©H01(Ω), q=1,2. For nonsmooth initial data, i.e., vâL2(Ω), the optimal L2(Ω)-norm error estimate requires an additional assumption on mesh, which is known to be satisfied for symmetric meshes. A quasi-optimal Lâ(Ω)-norm error estimate is also obtained. Further, we analyze two fully discrete schemes using convolution quadrature in time based on the backward Euler and the second-order backward difference methods, and derive error estimates for smooth and nonsmooth data. Finally, we present several numerical examples to confirm our theoretical results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 132, October 2018, Pages 73-90
Journal: Applied Numerical Mathematics - Volume 132, October 2018, Pages 73-90
نویسندگان
Mariam Al-Maskari, Samir Karaa,