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**A new positive definite expanded mixed finite element method for parabolic integrodifferential equations.**
*(English)*
Zbl 1251.65140

Summary: A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

### MSC:

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

65R20 | Numerical methods for integral equations |

35K99 | Parabolic equations and parabolic systems |

45K05 | Integro-partial differential equations |

### Keywords:

positive definite expanded mixed finite element method; parabolic partial integrodifferential equations
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\textit{Y. Liu} et al., J. Appl. Math. 2012, Article ID 391372, 24 p. (2012; Zbl 1251.65140)

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### References:

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