This paper generalizes earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. These results require a strong form of well‐posedness and a stability analysis in the $L_{\infty }$ norm for the meshfree discretization. Since quasilinear problems are usually treated in Hölder norms, both aspects have to be transformed to the Hölder situation. This finally leads to error bounds and convergence rates, the latter being dependent on the smoothness of the true solution. The paper focuses on Dirichlet conditions and postpones other boundary conditions to a forthcoming paper. A numerical example is provided.

中文翻译：

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拟线性椭圆方程组无网格搭配方法的非线性离散化理论

本文将有关半线性椭圆二阶问题的无网格配置方法的早期结果推广到了拟线性情况。这些结果需要强有力的形式良好的定位和稳定性分析。${\mathrm{大号}}_{\infty }$无网格离散化的规范。由于准线性问题通常在Hölder规范中处理，因此这两个方面都必须转换为Hölder情况。这最终导致误差范围和收敛速度，后者取决于真实解的平滑度。本文着重于Dirichlet条件，并将其他边界条件推迟到即将发表的论文中。提供了一个数值示例。