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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
The lumped mass FEM for a time-fractional cable equation
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., v∈Hq(Ω)∩H01(Ω), q=1,2. For nonsmooth initial data, i.e., v∈L2(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 L∞(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
نویسندگان
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