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Quasi-least-squares finite element method for steady flow and heat transfer with system rotation

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Abstract

Two quasi-least-squares finite element schemes based on L 2 inner product are proposed to solve a steady Navier–Stokes equations, coupled to the energy equation by the Boussinesq approximation and augmented by a Coriolis forcing term to account for system rotation. The resulting nonlinear systems are linearized around a characteristic state, resulting in linearized least-squares models that yield algebraic systems with symmetric positive definite coefficient matrices. Existence of solutions are investigated and a priori error estimates are obtained. The performance of the formulation is illustrated by using a direct iteration procedure to treat the nonlinearities and shown theoretical convergent rate for general initial guess.

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Authors and Affiliations

  1. School of Mathematics and System Science, Shandong University, Jinan, 250100, People’s Republic of China

    Danping Yang

  2. Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, People’s Republic of China

    Liqiu Wang

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  1. Danping Yang
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  2. Liqiu Wang
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Correspondence to Danping Yang.

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Yang, D., Wang, L. Quasi-least-squares finite element method for steady flow and heat transfer with system rotation. Numer. Math. 104, 377–411 (2006). https://doi.org/10.1007/s00211-006-0019-0

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