Moving Mesh Methods For Partial Differential Equation: Advancing numerical solutions for time-dependent PDEs using moving mesh methods

Abstract

In the previous section, we have outlined the aims andsome techniques behind the generation of irregular grids. We now turn ourattention to methods which aim to move the mesh in time to solve non-steadydifferential equations. Whilst retaining the properties (and hence thenumerical benefits) of the ideas presented above. We shall make constantreference to the techniques in Section 2.1, so it makes sense to follow thesame order of events. starting with the use of the equidistribution principlein deriving moving mesh methods in one dimension.