Details of Grant 

EPSRC Reference:	GR/R76615/01
Title:	Anisotropic hp-Adaptive Finite Element Methods for Hyperbolic Conservation Laws
Principal Investigator:	Houston, Professor P
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Leicester
Scheme:	Advanced Fellowship (Pre-FEC)
Starts:	01 October 2002	Ends:	30 June 2005	Value (£):	228,485
EPSRC Research Topic Classifications:	Numerical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 19 Nov 2001 Maths AF & SF Sifting Panel Deferred 19 Dec 2001 MATHS AF INTERVIEW PANEL 2002 Deferred
Summary on Grant Application Form
The ever-increasing range of applications of nonlinear conservation laws of hyperbolic/nearly-hyperbolic type is a fertile source of difficult and challenging problems with important implications in engineering design; typical examples include the modelling of compressible viscous and inviscid fluid flows, as well as wave propagation in electromagnetic applications. Typically, solutions to these partial differential equations exhibit a wide range of localised structures, such as shock waves, contact discontinuities, boundary layers and rarefaction waves, and their numerical approximation presents a very challenging task. The key objective of this project to address the issue of solution quality; namely, how accurate is the numerical solution and how can the most accurate solution be attained for a fixed computational resource? To this end, the aim of the proposed research is to develop a comprehensive mathematical theory of anisotropic finite element methods which incorporate both local mesh subdivision and local polynomial enrichment. In particular, a priori and a posteriori error bounds will be established for families of finite element spaces consisting of shape-irregular (anisotropic) meshes with anisotropic polynomial degrees. Here, bounds on the discretisation error measured in terms of negative Sobolev norms, as well as for general target functionals of engineering interest, will be derived. Both linear and nonlinear problems will be considered.
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Organisation Website:	http://www.le.ac.uk