Abstract
We present numerically verified a posteriori estimates of the norms of inverse operators for linear parabolic differential equations. In case that the corresponding elliptic operator is not coercive, existing methods for a priori estimates of the inverse operators are not accurate and, usually, exponentially increase in time variable. We propose a new technique for obtaining the estimates of the inverse operator by using the finite dimensional approximation and error estimates. It enables us to obtain very sharp bounds compared with a priori estimates. We will give some numerical examples which confirm the actual effectiveness of our method.
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The authors have presented the results of this paper during the SCAN 2010 conference in Lyon, September 2010.
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Nakao, M.T., Kinoshita, T. & Kimura, T. On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems. Computing 94, 151–162 (2012). https://doi.org/10.1007/s00607-011-0180-x
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DOI: https://doi.org/10.1007/s00607-011-0180-x