An Analysis on Moving Mesh Methods for Non-Linear Partial Differential Equations: the Approximate Solution

Improving Efficiency and Accuracy in Solving Non-linear Partial Differential Equations using Moving Mesh Methods

Abstract

This study is primarily concerned with the use of moving mesh methods for the approximate solution of non-linear partial differential equations of parabolic type. Such methods have become a popular means for the solution of problems which may contain sharp features that are hard to approximate. Whilst efficiently managing computational overheads. Initially, a novel moving grid technique known as Contour Zoning is discussed. This 'static' method is able to reduce numerical resources by grouping together sets of nodes as a moving contour of the solution.