Local discontinuous Galerkin finite element method for the Caputo-type diffusion equation with variable coefficient
We present an efficient method for seeking the numerical solution of a Caputo-type diffusion equation with a variable coefficient.Since the solution of such an equation is likely to have a weak singularity near the initial time,the time-fractional derivative is discretized using the L1 formula on nonuniform meshes.For spatial derivative,we employ the local discontinuous Galerkin method to derive a fully discrete scheme.Based on a dis-crete fractional Gronwall inequality,the numerical stability and convergence of the derived scheme are proven which are both α-robust,that is,the bounds obtained do not blow up as α → 1-.Finally,numerical experiments are displayed to confirm the theoretical results.
local discontinuous Galerkin methodnonuniform time meshα-robustweak singularityvariable coefficient
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