标题： 单调半线性椭圆型偏微分方程具有次临界非线性的最优有限元逼近 显示英文标题

标题： Optimal finite element approximations of monotone semilinear elliptic PDE with subcritical nonlinearities

摘要： 我们研究了迭代有限元逼近方法，用于数值求解具有次临界增长的单调非线性反应的半线性椭圆边值问题。 我们的工作重点是关于一种在局部向多边形区域可能的角奇异性方向细化网格上的收缩型Picard迭代格式的最优先验误差估计。 我们的分析尤其涉及加权Sobolev空间中的椭圆正则性结果以及Trudinger不等式的使用，这对于处理次临界增长的非线性项至关重要。 一系列数值实验验证了我们方法的准确性和有效性。 显示英文摘要

摘要： We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori error estimate for a contractive Picard type iteration scheme on meshes that are locally refined towards possible corner singularities in polygonal domains. Our analysis involves, in particular, an elliptic regularity result in weighted Sobolev spaces and the use of the Trudinger inequality, which is instrumental in dealing with subcritically growing nonlinearities. A series of numerical experiments confirm the accuracy and efficiency of our method.