论文标题
椭圆问题阳性解决方案的数值验证方法
Numerical verification method for positive solutions of elliptic problems
论文作者
论文摘要
本文的目的是提出方法，以验证假设$ h^1_0 $ -ERROR估算$ \ left \ weft \ | U- \ hat {U} \ right \ right \ | ____ {h_ {0}}^{1}}^$ unim uniim and An uniim and umerim and An oniim and An错误绑定$ρ$。我们提供了充分的条件，使解决方案是正面的，并分析了我们在多项式非线性方面的椭圆形问题的应用范围。我们提供了数值示例，其中将我们的方法应用于一些重要问题。
The purpose of this paper is to propose methods for verifying the positivity of a weak solution $ u $ of an elliptic problem assuming $ H^1_0 $-error estimation $ \left\|u-\hat{u}\right\|_{H_{0}^{1}} \leq ρ$ given some numerical approximation $ \hat{u} $ and an explicit error bound $ ρ$. We provide a sufficient condition for the solution to be positive and analyze the range of application of our method for elliptic problems with polynomial nonlinearities. We present numerical examples where our method is applied to some important problems.
