论文标题
一种质量倾斜的有限元法，用于辐射的多维半线性热方程的径向对称溶液
A mass-lumping finite element method for radially symmetric solution of a multidimensional semilinear heat equation with blow-up
论文作者
论文摘要
这项研究提出了一种新的质量倾斜有限元方法，用于计算$ n $尺寸球（$ n \ ge 2 $）中半线性热方程的径向对称解。我们提供两个方案（ML-1）和（ML-2），并通过离散的最大原理得出其错误估计。在加权$ l^{2} $ norm中，（ML-1）的收敛处于最佳顺序，但（ML-2）的收敛仅在次优顺序上。然而，方案（ML-2）再现了原始方程的溶液的爆炸。实际上，在方案（ML-2）中，我们可以准确地近似爆炸时间。我们的理论结果在数值实验中得到了验证。
This study presents a new mass-lumping finite element method for computing the radially symmetric solution of a semilinear heat equation in an $N$ dimensional ball ($N\ge 2$). We provide two schemes, (ML-1) and (ML-2), and derive their error estimates through the discrete maximum principle. In the weighted $L^{2}$ norm, the convergence of (ML-1) was at the optimal order but that of (ML-2) was only at sub-optimal order. Nevertheless, scheme (ML-2) reproduces a blow-up of the solution of the original equation. In fact, in scheme (ML-2), we could accurately approximate the blow-up time. Our theoretical results were validated in numerical experiments.
