Moving mesh generation using the parabolic Monge–Ampère equation


Budd, C. J. and Williams, J. F., 2009. Moving mesh generation using the parabolic Monge–Ampère equation. SIAM Journal on Scientific Computing, 31 (5), pp. 3438-3465.

Related documents:

This repository does not currently have the full-text of this item.
You may be able to access a copy if URLs are provided below. (Contact Author)

Official URL:


This article considers a new method for generating a moving mesh which is suitable for the numerical solution of partial differential equations (PDEs) in several spatial dimensions. The mesh is obtained by taking the gradient of a (scalar) mesh potential function which satisfies an appropriate nonlinear parabolic partial differential equation. This method gives a new technique for performing r-adaptivity based on ideas from optimal transportation combined with the equidistribution principle applied to a (time-varying) scalar monitor function (used successfully in moving mesh methods in one-dimension). Detailed analysis of this new method is presented in which the convergence, regularity, and stability of the mesh is studied. Additionally, this new method is shown to be straightforward to program and implement, requiring the solution of only one simple scalar time-dependent equation in arbitrary dimension, with adaptivity along the boundaries handled automatically. We discuss three preexisting methods in the context of this work. Examples are presented in which either the monitor function is prescribed in advance, or it is given by the solution of a partial differential equation.


Item Type Articles
CreatorsBudd, C. J.and Williams, J. F.
DepartmentsFaculty of Science > Mathematical Sciences
ID Code17157


Actions (login required)

View Item