A XFEM Lagrange Multiplier Technique for Stefan Problems

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Table of contents

1 Introduction 
1.1 Motivation
1.2 Thesis Contribution and Novelty
1.3 Thesis Organization
2 Literature Review 
2.1 Introduction
2.2 Interface Handling Techniques
2.3 Stefan Problem
2.4 Navier-Stokes Equations
3 The Extended Finite Element Method 
3.1 Introduction
3.2 Enrichment Strategies
3.3 Dirichlet Boundary Conditions
3.4 Numerical Integration
3.5 The Level Set Method
4 A XFEM Lagrange Multiplier Technique for Stefan Problems
4.1 Resumé
4.2 Abstract
4.3 Introduction
4.4 Governing Equations
4.5 Numerical Implementation
4.6 Results
4.7 Conclusion
5 A XFEM Phase Change Model with Convection
5.1 Resumé
5.2 Abstract
5.3 Introduction
5.4 Governing Equations
5.5 Numerical Implementation
5.6 Results
5.7 Conclusion
6 Modelling of Phase Change with Non-Constant Density using XFEM and a Lagrange Multiplier
6.1 Resumé
6.2 Abstract
6.3 Introduction
6.4 Governing Equations
6.5 Numerical Implementation
6.6 Results
6.7 Conclusion
7 Conclusion