<p>We propose a quantitative lower bound estimates for the norm of resolvent using Galerkin approximation in this paper. As an application, we describe the a posteriori error estimates of the norm of resolvent and the norm of Galerkin approximate operator. An exact norm of resolvent can be obtained from numerical examples, and this a posteriori error estimates may be the optimal order.</p>

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Quantitative lower bounds estimates for the norm of resolvent using Galerkin approximation and its applications

  • Takehiko Kinoshita,
  • Yoshitaka Watanabe,
  • Mitsuhiro T. Nakao

摘要

We propose a quantitative lower bound estimates for the norm of resolvent using Galerkin approximation in this paper. As an application, we describe the a posteriori error estimates of the norm of resolvent and the norm of Galerkin approximate operator. An exact norm of resolvent can be obtained from numerical examples, and this a posteriori error estimates may be the optimal order.