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We consider a fully discrete H1-Galerkin mixed finite element approximation of one nonlinear integrodifferential model which often arises in mathematical modeling of the process of a magnetic field penetrating into a substance. We adopt the Crank-Nicolson discretization for time derivative. Optimal order a priori error estimates for the unknown function in L2 and H1 norm and its gradient function in L2 norm are presented. A numerical example is given to verify the theoretical results

abstract and applied analysis

Crank-Nicolson Fully Discrete<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>-Galerkin Mixed Finite Element Approximation of One Nonlinear Integrodifferential Model

Crank-Nicolson Fully DiscreteH1-Galerkin Mixed Finite Element Approximation of One Nonlinear Integrodifferential Model