Time discretization of parabolic problems by the discontinuous Galerkin method. (English) Zbl 0589.65070
The authors analyze the discontinuous Galerkin method for the time discretization of parabolic type problems \(y_ t+Ay=f\) for \(t\geq 0\), \(y(0)=y_ 0\), where y is a function of t with values in a Hilbert space H, A is a self-adjoint positive definite linear operator on H (independent of t), and \(y_ 0\) and \(f=f(t)\) are given data. Error estimates are derived at the nodal points as well as uniformly in time for smooth and non-smooth initial data. These estimates are then combined with known estimates for semi-discrete in space Galerkin approximations of parabolic problems to yield error estimates for complete discretizations of such problems.
Reviewer: W.Ames
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35G10 | Initial value problems for linear higher-order PDEs |
| 35K25 | Higher-order parabolic equations |
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