Stabilised fine element methods for fictitious domain problems

Rights statement
Awarding institution
  • University of Strathclyde
Date of award
  • 2017
Thesis identifier
  • T14694
Person Identifier (Local)
  • 201264597
Qualification Level
Qualification Name
Department, School or Faculty
  • This thesis deals with the solution of the Laplace and heat equations on complicated domains. The approach follows the idea of the fictitious domain method, in which a larger (simpler) domain is introduced with the idea of avoiding the use of meshes that resolve the geometry. The first part of the thesis is dedicated to propose and analyse a new stabilised finite element method for the heat equation. The analysis, not available to date, is based on the introduction of a new projected initial condition that satisfies the boundary conditions of the original problem weakly. This allows us to prove inconditional stability and optimal convergence of the solution, thus avoiding the restriction linking the time discretisation and mesh width parameters present in previous references. In the second part of this thesis the methodology has been adapted and extended to cover the case in which the problem at hand is posed in a domain containing several inclusions of small size. For this case, the usual fictitious domain approach is no longer applicable, and then a new method that compensates for the lack of stability of the original one is proposed, analysed and tested numerically. The numerical analysis has been carried out for the steady state case, but its applicability to time dependent problems is sketched and shown by means of numerical experiments.
Advisor / supervisor
  • Barrenechea, Gabriel R.
Resource Type
  • Previously held under moratorium from 11 September 2017 until 17 February 2022
Date Created
  • 2017
Former identifier
  • 9912566793102996