Abstract
This paper presents a new numerical method to obtain the rigorous upper bounds of inverse linear elliptic operators. The invertibility of a linearized operator and its norm estimates give important informations when analyzing the nonlinear elliptic partial differential equations (PDEs). The computational costs depend on the concerned elliptic problems as well as the approximation properties of used finite element subspaces, e.g., mesh size or so. We show the proposed new estimate is effective for an intermediate mesh size.
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Acknowledgments
The authors are very grateful to two anonymous reviewers. This work was supported by the Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 23740074, No. 24340018, and No. 24540151) and supported by Program for Leading Graduate Schools “Training Program of Leaders for Integrated Medical System for Fruitful Healthy-Longevity Society.”
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Kinoshita, T., Watanabe, Y., Nakao, M.T. (2016). Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators. In: Nehmeier, M., Wolff von Gudenberg, J., Tucker, W. (eds) Scientific Computing, Computer Arithmetic, and Validated Numerics. SCAN 2015. Lecture Notes in Computer Science(), vol 9553. Springer, Cham. https://doi.org/10.1007/978-3-319-31769-4_18
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DOI: https://doi.org/10.1007/978-3-319-31769-4_18
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