»ã±¨±êÌâ (Title)£ºThe direct discontinuous Galerkin method for a time-fractional initial-boundary value problem (¹¦·ò·ÖÊý½×³õÖµÎÊÌâµÄÖ±½Ó¼ä¶ÏGalerkin²½Öè)

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»ã±¨¹¦·ò (Time)£º2022Äê10ÔÂ13ÈÕ(ÖÜËÄ) 8:30-10:00

»ã±¨µØÖ· (Place)£ºÏßÉÏÌÚѶ»áÒ飨»áÒé ID£º378 158 995£©

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»ã±¨ÌáÒª£ºIn this talk, a fully discrete numerical method for the time-fractional reaction-diffusion initial-boundary value problem with a weak singularity solution is investigated, where we use the well-known L1 discretization on a graded mesh in time and a direct discontinuous Galerkin (DDG) finite element method on a uniform mesh in space. For the linear case with the periodic boundary condition, we prove that at each time level of the mesh, our L1-DDG solution is superconvergent of order k+2 in L^2 (¦¸) to a particular projection of the exact solution. Moreover, the L1-DDG solution achieves superconvergence of order (k+2) in a discrete L^2 (¦¸) norm computed at the Lobatto points, and order (k+1) superconvergence in a discreteH^1 (¦¸) seminorm at the Gauss points. For the nonlinear case with Dirichlet boundary conditions, we derive the unconditionally optimal L^2 (¦¸) norm convergent result by using the time-space splitting technical. Finally, numerical results show that our analysis is sharp.