Details of Grant 

EPSRC Reference:	EP/D058791/1
Title:	Scale Invariant Moving Mesh Finite Elements for Multidimensional Nonlinear Partial Differential Equations
Principal Investigator:	Hubbard, Professor M
Other Investigators:	Jimack, Professor PK
Researcher Co-Investigators:
Project Partners:
Department:	Sch of Computing
Organisation:	University of Leeds
Scheme:	Mathematics Small Grant PreFEC
Starts:	01 December 2005	Ends:	30 November 2008	Value (£):	5,284
EPSRC Research Topic Classifications:	Non-linear Systems Mathematics Numerical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
Many physical and chemical processes, typified by those related to fluid flow, can be modelled mathematically using partial differential equations. These can usually only be solved in the simplest of situations, but solutions in far more complex cases can be approximated using numerical and computational techniques. Traditional approaches to providing these computational simulations have typically modelled the evolution of these processes by approximating them on a uniform mesh of points on domains with fixed boundaries. However, many situations (consider a spreading droplet, for example) naturally suggest a domain which evolves with the flow, while others (say the movement of a shock wave up and down an aeroplane wing) have their main focus of interest in following the motion of a sharp internal feature. For accuracy and efficiency a computational method should dictate the movement of the mesh accordingly.This project aims to enhance and analyse a new computational method developed recently by the applicants to incorporate these ideals, which has already shown the ability to model complex situations. Furthermore, the method has been designed so that the approximation preserves inherent properties (such as conservation principles and invariances) of the mathematical model being used to predict the fluid flow. The long term aim is a method which can reliably and accurately predict a range of fluid flows involving moving boundaries or internal features, from the spreading of droplets, through waves breaking on a beach, to chemical explosions.
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Organisation Website:	http://www.leeds.ac.uk