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.

翻译：本研究提出了一种新的大规模排除有限要素方法,用于计算半线性热方程式在美元元体球中的半线性对称解决方案(NN\Ge 2$)。我们提供了两种方案(ML-1和(ML-2),并通过离散最大原则得出错误估计。在加权的$L%2}标准中,(ML-1)的趋同处于最佳状态,但(ML-2)的趋同仅处于次最佳状态。然而,(ML-2)方案(ML-2)重复了最初方程式的解答。事实上,在方案(ML-2)中,我们可以准确估计出打击时间。我们的理论结果在数字实验中得到了验证。