A Comparative Study of Finite Difference and Finite Element Methods for Solving Nonlinear Heat Conduction Equations
Year: 2026
Type: article
Abstract: A few examples of the numerous mathematical physics and engineering applications that depend on a knowledge of nonlinear heat conduction equations include thermal analysis of materials, energy systems, and fluid-structure interactions. These are just a few examples. When it comes to predicting proper solutions in nonlinear applications, numerical techniques are absolutely necessary since closed-form solutions are often unavailable. This research investigates and contrasts two well-known procedures, namely the finite element method (FEM) and the finite difference method (FDM). Both of these methods are widely used in the field. Once the nonlinear heat conduction equation has been discretized using any of the two methodologies, iterative solvers are used in order to deal with the nonlinearity that is present in the analysis. Evaluations are carried out in a methodical manner, with factors such as accuracy, computational efficiency, convergence, and stability being taken into consideration. Case studies of nonlinear conduction problems in one and two dimensions, with varying boundary and starting conditions, are included into the research project. In order to determine how each method works, we conduct numerical experiments. Additionally, where it is feasible, we compare the error estimates to benchmark solutions in order to see how well they compare. Based on these findings, it should be clear that FDM performs well in domains that are well-organized and have geometries that are not too difficult. However, FEM is far more adaptable when it comes to coping with complex boundaries and irregular meshes. Furthermore, this study contributes to the clarification of numerical techniques for nonlinear partial differential equations (PDEs) and provides helpful advice for the use of these methods in scientific and engineering simulations.
Author: Mr. Sanjay Sharma
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7217945998