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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