非线性Sobolev-Galpern型湿气迁移方程的最低阶非协调混合元收敛性分析

Convergence Analysis of the Lowest Nonconforming Mixed Finite Element for Nonlinear Sobolev-Galpern Type Equations of Moisture Migration

对一类非线性Sobolev-Galpern型湿气迁移方程利用非协调线性三角形元和 P 0×P 0 元,构造一个新的低阶非协调混合元格式,并证明逼近格式解的存在唯一性.同时,在抛弃传统混合元分析的必要工具 Ritz 投影的前提下,直接利用单元特性,分别得到原始变量u 的H^1 模意义下和中间变量P =-(a(u)▽ut + b(u)▽u)的L^2 模意义下的最优误差估计.

Based on the nonconforming linear triangular finite element, the lowest noconforming mixed finite element approximate scheme is established for nonlinear Sobolev-Galpern type equations of moisture migration. The existence and uniqueness of approximation solution are proved. At the same time, without the conventional Ritz projection, the optimal error estimates of exact solution u in H^1 - norm and intermediate variable P =-(a(u)▽ut + b(u)▽u) in L^2 - norm are deduced by some special properties of the elements.