Abstract/Summary

In this thesis we consider a class of conservation based moving mesh methods applied to hyperbolic conservation laws. We mainly concentrate on the one dimensional case with the examples of the linear advection equation, inviscid Burgers’ equation and the Buckley-Leverett equation. The moving mesh methods are generated using the conservation of mass as a method for determining the mesh velocity at the computational nodes. We use the notion of the reference space as a mathematical tool to analyse the moving mesh methods allowing us to show the accuracy, stability conditions and convergence. In addition we use the reference space as a technique for constructing new moving mesh methods which share the accuracy and stability properties of the fixed mesh scheme they are derived from. At the end of the thesis we use the knowledge gained from the scalar conservation laws to construct moving mesh methods for the isothermal equations.