Weakly Consistent Regularisation Methods for Ill-Posed Problems

  • Erik BurmanEmail author
  • Lauri Oksanen
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 15)


This Chapter takes its origin in the lecture notes for a 9 h course at the Institut Henri Poincaré in September 2016. The course was divided in three parts. In the first part, which is not included herein, the aim was to first recall some basic aspects of stabilised finite element methods for convection-diffusion problems. We focus entirely on the second and third parts which were dedicated to ill-posed problems and their approximation using stabilised finite element methods. First we introduce the concept of conditional stability. Then we consider the elliptic Cauchy-problem and a data assimilation problem in a unified setting and show how stabilised finite element methods may be used to derive error estimates that are consistent with the stability properties of the problem and the approximation properties of the finite element space. Finally, we extend the result to a data assimilation problem subject to the heat equation.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK

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