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A new error estimate for a fully finite element discretization scheme for parabolic equations using Crank-Nicolson method. (English) Zbl 1340.65199
The paper deals with the numerical solution of the heat equation with the aid of the finite element method for the space semi-discretization and the Crank-Nicolson scheme for the time discretization. The authors derive a priori error estimates in the discrete \(W^{1,\infty}(0,T; L^2(\Omega))\)-norm and in the discrete \(L^{\infty}(0,T; H^1_0(\Omega))\)-seminorm. The estimates are optimal with respect to the space as well as time coordinates.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
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
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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