Summary.
We investigate the convergence of difference schemes for the one-dimensional heat equation when the coefficient at the time derivative (heat capacity) is \(c\left( x\right) =1+K\delta \left( x-\xi \right). K = \const > 0\) represents the magnitude of the heat capacity concentrated at the point \(x=\xi\). An abstract operator method is developed for analyzing this equation. Estimates for the rate of convergence in special discrete energetic Sobolev's norms, compatible with the smoothness of the solution are obtained.
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Received November 2, 1999 / Revised version received July 24, 2000 / Published online May 4, 2001
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Jovanovic, B., Vulkov, L. On the convergence of finite difference schemes for the heat equation with concentrated capacity. Numer. Math. 89, 715–734 (2001). https://doi.org/10.1007/s002110100280
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DOI: https://doi.org/10.1007/s002110100280