论文标题
对椭圆边界值问题的阳性的后验验证
A posteriori verification of the positivity of solutions to elliptic boundary value problems
论文作者
论文摘要
本文的目的是开发一种统一的后验方法，用于通过假设$ h^2 $ regularity也不是$ l^{\ infty} $ eRROR估算来验证椭圆边界值问题的积极性，而只有$ h^1_0 $ -Error估计。在[J。计算。应用。数学，卷。 370，（2020）112647]，我们提出了两种方法来验证几个半线性椭圆边界值问题的溶液的阳性。但是，某些情况需要$ l^{\ infty} $ eRROR估计，因此需要狭窄的适用性。在本文中，我们扩展了其中一种方法，并将其与Laplacian特征值的先验误差范围结合在一起，以获得具有广泛应用的统一方法。我们描述了如何评估一些验证所需溶液阳性所需的常数。我们将方法应用于几个问题，包括以前的方法不适用的问题。
The purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions of elliptic boundary value problems by assuming neither $H^2$-regularity nor $ L^{\infty} $-error estimation, but only $ H^1_0 $-error estimation. In [J. Comput. Appl. Math, Vol. 370, (2020) 112647], we proposed two approaches to verify the positivity of solutions of several semilinear elliptic boundary value problems. However, some cases require $ L^{\infty} $-error estimation and, therefore, narrow applicability. In this paper, we extend one of the approaches and combine it with a priori error bounds for Laplacian eigenvalues to obtain a unified method that has wide application. We describe how to evaluate some constants required to verify the positivity of desired solutions. We apply our method to several problems, including those to which the previous method is not applicable.
