| EPSRC Reference: |
GR/R76615/02 |
| Title: |
Anisotropic hp-Adaptive Finite Element Methods for Hyperbolic Conservation Laws |
| Principal Investigator: |
Houston, Professor P |
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| Department: |
Sch of Mathematical Sciences |
| Organisation: |
University of Nottingham |
| Scheme: |
Advanced Fellowship (Pre-FEC) |
| Starts: |
01 July 2005 |
Ends: |
30 September 2007 |
Value (£): |
112,942
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Summary on Grant Application Form |
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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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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.nottingham.ac.uk |