A stabilizer-free weak Galerkin finite element method with Alikhanov formula on nonuniform mesh for a linear reaction-subdiffusion problem. (English) Zbl 1538.65377
Summary: 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.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference 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 |
| 35R11 | Fractional partial differential equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 26A33 | Fractional derivatives and integrals |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
Keywords:
linear reaction-subdiffusion problem; stabilizer-free weak Galerkin finite element method; nonuniform time mesh; error estimateReferences:
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