Mixed finite element methods for nonlinear second-order elliptic problems
Mixed finite element methods for nonlinear second-order elliptic problems
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DOI：
10.1137/0732040
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发表时间：
1995-06
影响因子：
2.9
通讯作者：
Eun‐Jae Park
中科院分区：
文献类型：
--
作者：
Eun‐Jae Park
对最一般的拟线性二阶椭圆型算子的散度型Dirichlet问题，给出了混合有限元方法。证明了逼近的存在唯一性，并证明了用该方法逼近的标量函数和向量函数的最优误差估计在L^2 $内。误差估计也在$L^q $，$2 \leq q \leq + \infty $中导出。提出并分析了求解非线性代数方程组的牛顿法。
Mixed finite element methods are developed to approximate the solution of the Dirichlet problem for the most general quasi-linear second-order elliptic operator in divergence form. Existence and uniqueness of the approximation are proved, and optimal error estimates in $L^2 $ are demonstrated for both the scalar and vector functions approximated by the method. Error estimates are also derived in $L^q $, $2 \leq q \leq + \infty $. Newton’s method is presented and analyzed to solve the nonlinear algebraic equations.