Second order fully discrete defect‐correction scheme for nonstationary conduction‐convection problem at high  R eynolds number | Zendy

Su Haiyan | Zendy; Feng Xinlong | Zendy; He Yinnian | Zendy

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Second order fully discrete defect‐correction scheme for nonstationary conduction‐convection problem at high R eynolds number

Author(s) -

Su Haiyan,

Feng Xinlong,

He Yinnian

Publication year - 2017

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.22115

Subject(s) - mathematics , thermal conduction , nonlinear system , grid , stability (learning theory) , scheme (mathematics) , partial differential equation , reynolds number , viscosity , partial derivative , convection , crank–nicolson method , finite element method , mathematical analysis , mechanics , geometry , computer science , thermodynamics , physics , quantum mechanics , machine learning , turbulence

This survey enfolds rigorous analysis of the defect‐correction finite element (FE) method for the time‐dependent conduction‐convection problem which based on the Crank‐Nicolson scheme. The method consists of two steps: solve a nonlinear problem with an added artificial viscosity term on a FE grid and correct the solutions on the same grid using a linearized defect‐correction technique. The stability and optimal error estimate of the fully discrete scheme are derived. As a consequence, the effectiveness of the method to deal with high Reynolds number is illustrated in several numerical experiments. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 681–703, 2017

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