Analysis of multiscale mortar mixed approximation of nonlinear elliptic equations
Analysis of multiscale mortar mixed approximation of nonlinear elliptic equations
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非线性椭圆方程多尺度砂浆混合逼近分析
DOI：
10.1016/j.camwa.2017.09.031
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Dong
中科院分区：
文献类型：
--
作者：
M. Arshad;Eun‐Jae Park;Dong
建立了一种逼近非线性二阶椭圆型方程的多尺度砂浆混合有限元方法。该方法是基于非重叠区域分解和砂浆有限元方法。证明了该近似解的存在唯一性，并得到了速度和压力的先验L误差估计。证明了砂浆压力的一个误差界。迫击炮压力的收敛估计是基于具有离散压力依赖系数的线性界面公式。通过适当地选择迫击炮空间和多项式逼近次数，在精细尺度上实现了最优阶收敛。证明了非线性代数系统的牛顿-拉夫森方法是二次收敛的。数值实验验证了理论结果的正确性。
A multiscale mortar mixed finite element method is established to approximate non-linear second order elliptic equations. The method is based on non-overlapping domain decomposition and mortar finite element methods. The existence and uniqueness of the approximation are demonstrated, and a priori L 2-error estimates for the velocity and pressure are derived. An error bound for mortar pressure is proved. Convergence estimates of the mortar pressure are based on a linear interface formulation having the discrete-pressure dependent coefficient. Optimal order convergence is achieved on the fine scale by a proper choice of mortar space and polynomial degree of approximation. The quadratic convergence of the Newton–Raphson method is proved for the nonlinear algebraic system arising from the mortar mixed formulation of the problem. Numerical experiments are performed to support theoretic results.