A new error estimate for a fully finite element discretization scheme for parabolic equations using Crank-Nicolson method
Abdallah Bradji, Jürgen Fuhrmann (2014)
Mathematica Bohemica
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Finite element methods with piecewise polynomial spaces in space for solving the nonstationary heat equation, as a model for parabolic equations are considered. The discretization in time is performed using the Crank-Nicolson method. A new a priori estimate is proved. Thanks to this new a priori estimate, a new error estimate in the discrete norm of is proved. An -error estimate is also shown. These error estimates are useful since they allow us to get second order time accurate approximations...