Nitsche-XFEM for a time fractional diffusion interface problem. (English) Zbl 1541.65112
Summary: In this paper, we propose a space-time finite element method for a time fractional diffusion interface problem. This method uses the low-order discontinuous Galerkin (DG) method and the Nitsche extended finite element method (Nitsche-XFEM) for temporal and spatial discretization, respectively. Sharp pointwise-in-time error estimates in graded temporal grids are derived, without any smoothness assumptions on the solution. Finally, three numerical examples are provided to verify the theoretical results.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
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