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A new mixed finite element analysis for pseudo-parabolic intergo-differential equation. (Chinese. English summary) Zbl 1399.65247

Summary: A new mixed finite element pattern for pseudo-parabolic integro-differential equation is studied. Through Bramble-Hilbert lemma, the spaces of incomplete biquadratic element \(Q_2^- \) and its gradient are explored. A new high precision theory on element is proved. The superclose properties for the primitive variable \(u\) in \({H^1}\)-norm and the intermediate variable \(\boldsymbol{p}\) in \({L^2}\)-norm are obtained respectively for semi-discrete and the backward Euler fully discrete schemes.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R09 Integro-partial differential equations
35S11 Initial-boundary value problems for pseudodifferential operators (MSC2010)
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