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Mixed discontinuous Galerkin analysis of thermally nonlinear coupled problem

机译:热非线性耦合问题的混合不连续Galerkin分析

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摘要

A stabilized mixed discontinuous Galerkin (SMDG) method based on Brezzi-Hughes-Marini-Masud [F. Brezzi, T.J.R. Hughes, L.D. Marini, A. Masud, Mixed discontnuous Galerkin methods for Darcy flow, J. Sci. Comput. 22 (2005) 119-145.] is proposed to solve a thermally coupled nonlinear elliptic system modeling a large class of engineering problems. A fixed point algorithm is adopted to solve the nonlinear systems. Convergence analysis and error estimates are presented for equal order linear or bilinear discontinuous Lagrangian finite element interpolations for all fields. Numerical results are presented confirming the predicted convergence rates and illustrating the performance of the proposed formulation solving problems with globally stable and blowing up solutions.
机译:基于Brezzi-Hughes-Marini-Masud的稳定的混合不连续Galerkin(SMDG)方法[F.布雷兹(T.J.R.)休斯(L.D.) Marini,A。Masud,达西流的混合不连续Galerkin方法,J。Sci。计算[22(2005)119-145。]被提出来解决建模大量工程问题的热耦合非线性椭圆系统。采用定点算法求解非线性系统。针对所有领域的等阶线性或双线性不连续拉格朗日有限元插值,给出了收敛性分析和误差估计。给出的数值结果证实了预测的收敛速度,并说明了所提出的配方解决方案具有整体稳定和爆炸性问题的性能。

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