# Finite element method for radially symmetric solution of a multidimensional semilinear heat equation

## TL;DR

This paper develops and analyzes a finite element method for solving radially symmetric solutions of multidimensional semilinear heat equations, providing error estimates and validating results through numerical examples.

## Contribution

It introduces optimal error estimates for finite element solutions of semilinear heat equations with radial symmetry, including both symmetric and nonsymmetric formulations.

## Key findings

- Optimal order error estimates in $L^
Infty$ and weighted $L^2$ norms.
- Validation of theoretical results through numerical examples.

## Abstract

This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinear heat equations. In particular, this study establishes optimal order error estimates in $L^\infty$ and weighted $L^2$ norms for the symmetric and nonsymmetric formulation, respectively. Some numerical examples are presented to validate the obtained theoretical results.