## 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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### References:

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