Displaying similar documents to “On a method for a-posteriori error estimation of approximate solutions to parabolic problems”

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 𝒲 1 , ∞ ( ℒ 2 ) is proved. An ℒ ∞ ( ℋ 1 ) -error estimate is also shown. These error estimates are useful since they allow us to get second order time accurate approximations...

Grid adjustment based on a posteriori error estimators

Karel Segeth (1993)

Applications of Mathematics

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The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.