Discontinuous Galerkin finite element method for parabolic problems. (English) Zbl 1111.65087
The authors develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of \(| | u_t(t)| | _{L_2(\Omega)}=| | u_t| | _2\), for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. They give optimal convergence rates in both time and spatial variables.
Reviewer: Jialin Hong (Beijing)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
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