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We develop a temporally second-order stabilizer-free weak Galerkin (SFWG) finite element method with unequal time steps for reaction-subdiffusion equation in multiple space dimensions. In consideration of initial singularity of the solution, we prove a sharp error estimate on nonuniform time steps by two tools: discrete fractional Grönwall inequality and error convolution structure analysis. Furthermore, the fully discrete scheme achieves second-order accuracy in time by employing the graded temporal partition. Several numerical experiments are included to confirm the sharpness of theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study the multigrid algorithm for a quad-curl problem based on C 0 interior penalty method on bounded polygonal domains. It is shown that the contraction numbers of W -cycle multigrid algorithm for the C 0 interior penalty method converge uniformly with rate of m − α , where m is the number of pre-smoothing (and post-smoothing) steps, α is the index of elliptic regularity. The performance of the multigrid fast solver is illustrated by numerical results. [ABSTRACT FROM AUTHOR]