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arXiv · 1708.06322

Rigorous a-posteriori analysis using numerical eigenvalue bounds in a surface growth model

Christian Nolde·Dirk Blömker
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Abstract

In order to prove numerically the global existence and uniqueness of smooth solutions of a fourth order, nonlinear PDE, we derive rigorous a-posteriori upper bounds on the supremum of the numerical range of the linearized operator. These bounds also have to be easily computable in order to be applicable to our rigorous a-posteriori methods, as we use them in each time-step of the numerical discretization. The final goal is to establish global bounds on smooth local solutions, which then establish global uniqueness.

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Christian Nolde, Dirk Blömker. 2017-08-21. Rigorous a-posteriori analysis using numerical eigenvalue bounds in a surface growth model. https://arxiv.org/abs/1708.06322

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