In this paper, we prove the convergence and quasi-optimality of an adaptive finite element method for semilinear elliptic problems on errors by keeping sufficiently mildly graded meshes. Additional refinements are made to keep the meshes sufficiently mildly graded, but we find that it does not compromise the quasi-optimality of the adaptive finite element method presented in this paper. Numerical examples are provided to illustrate our theoretical results.

中文翻译：

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L2误差上半线性椭圆问题的自适应有限元方法的收敛性和拟最优性

在本文中，我们通过保持足够温和的渐变网格来证明自适应有限元方法对误差的半线性椭圆问题的收敛性和准最优性。进行了额外的改进以保持网格足够温和的分级，但我们发现它不会影响本文提出的自适应有限元方法的准最优性。提供了数值例子来说明我们的理论结果。