对一类非线性问题的空间分解算法证明了两个几何收敛性定理，改进了已有的结果。
Two geometrical convergence theorems of a space decomposition method for solving a kind of nonlinear problems have been proved, which are improvements of existing results.
应用正则分解和弱正则分解理论，我们同样获得了该算法在加权范数意义下的几何收敛性。
By applying the theories of regular splitting and weak regular splitting of matrices to the two considered algorithms, we obtain the weighted max-norm bounds for iterations too.
计算结果表明，广义协调元对于求解结构几何非线性问题同样具有精度高、收敛快等优点。
Numerical results indicate that the generalized conforming element has the advantages of high accuracy and uniform convergence to geometrically nonlinear problem of structures.
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