Abstract
In this paper the numerical solution of the two-dimensional heat conduction equation is investigated, by applying Dirichlet boundary condition at the upper side and Neumann boundary condition to the left, right, and lower sides. To the discretization in space, we apply the linear finite element method and for the time discretization the well-known theta-method. The aim of the work is to derive an adequate numerical solution for the homogeneous initial condition by this approach. We theoretically analyze the possible choices of the time-discretization step-size and establish the interval where the discrete model can reliably describe the original physical phenomenon.
As the discrete model, we arrive at the task of the one-step iterative method. We point out that there is a need to obtain both lower and upper bounds of the time-step size to preserve the qualitative properties of the real physical solution. The main results of the work is determining the interval for the time-step size to be used in this special finite element method and analyzing the main qualitative characterstics of the model. Our theoretical results are verified by different numerical experiments.
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Szabó, T. (2010). On the Discretization Time-Step in the Finite Element Theta-Method of the Two-Dimensional Discrete Heat Equation. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_75
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DOI: https://doi.org/10.1007/978-3-642-12535-5_75
Publisher Name: Springer, Berlin, Heidelberg
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