非线性湿气迁移方程的非协调EQ_1^(rot)元的超收敛分析

Superconvergence Analysis of the Nonconforming EQ_1^(rot) Element for Nonlinear Moisture Migration Equation

将EQ_1^(rot)非协调元应用于非线性Sobolev-Galpern型湿气迁移方程.利用平均值技巧及EQ_1^(rot)元的两个特殊性质:(I)当精确解属于H^3(Ω)时,在能量模意义下其相容误差比插值误差高一阶;(II)其插值算子与Ritz投影算子等价,得到了解的超逼近性质.进而,借助于插值后处理技术,导出了整体超收敛结果.

The nonconforming EQ1^rot element was applied to a kind of nonlinear moisture migration equation. The supercloseness property was obtained by using mean-value approach and two special properties of this element： （I） the consistency error is one order higher than its interpolation error in the energy norm when the exact solution belongs to H3 （O） ; （II） the interpolation operator is equivalent to its Ritz-projection operator. Fur- thermore, through interpolation post-processing technique, the global superconvergence result was derived.