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- W2267852856 abstract "We propose a piecewise-linear, time-stepping discontinuous Galerkin method to solve numerically a time fractional diffusion equation involving Caputo derivative of order μ ∈ (0, 1) with variable coefficients. For the spatial discretization, we apply the standard continuous Galerkin method of total degree ≤ 1 on each spatial mesh elements. Well-posedness of the fully discrete scheme and error analysis will be shown. For a time interval (0, T) and a spatial domain Ω, our analysis suggest that the error in $L^{2}left ((0,T),L^{2}({Omega })right )$ -norm is $O(k^{2-frac {mu }{2}}+h^{2})$ (that is, short by order $frac {mu }{2}$ from being optimal in time) where k denotes the maximum time step, and h is the maximum diameter of the elements of the (quasi-uniform) spatial mesh. However, our numerical experiments indicate optimal O(k 2 + h 2) error bound in the stronger $L^{infty }left ((0,T),L^{2}({Omega })right )$ -norm. Variable time steps are used to compensate the singularity of the continuous solution near t = 0." @default.
- W2267852856 created "2016-06-24" @default.
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- W2267852856 date "2016-02-13" @default.
- W2267852856 modified "2023-09-27" @default.
- W2267852856 title "A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients" @default.
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- W2267852856 doi "https://doi.org/10.1007/s11075-016-0106-y" @default.
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