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A new mixed finite element method based on the Crank-Nicolson scheme for the parabolic problems. (English) Zbl 1252.65170
Summary: We present a new mixed finite element method based on the less regularity of flux (velocity) for the parabolic problems in practice. Based on this new formulation, we give its corresponding stable conforming finite element approximation for the $P_0^2-P_{1}$ pair by using Crank-Nicolson time-discretization scheme. Moreover, we derive optimal error estimates in $H^{1}$-norm and $L^{2}$-norm for the approximation of pressure p and in $L^{2}$-norm for the approximation of velocity $u$. Finally, we give some numerical experiments to verify the efficiency and the theoretical results of the new mixed method.

65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
Full Text: DOI
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