| EPSRC Reference: |
EP/L022745/1 |
| Title: |
Virtual Element Method (VEM) |
| Principal Investigator: |
Cangiani, Dr A |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
10 July 2014 |
Ends: |
31 May 2016 |
Value (£): |
98,961
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| Environment |
Pharmaceuticals and Biotechnology |
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Summary on Grant Application Form |
We propose to develop the Virtual Element Method (VEM), a novel paradigm for the numerical solution of Partial Differential Equations (PDEs).
The VEM is an extremely flexible mesh based method allowing for the use of general polygonal/polyhedral meshes including non-convex, degenerate, and non-matching elements. It is a unifying framework from which L2, H1, H2, H(div), and H(curl) elements can be naturally constructed. In particular, the VEM can deliver highly regular solutions, hence proving better suited than standard finite element techniques for the solution of higher-order problems and eigenvalues approximation.
The VEM trial functions are solutions of suitable partial differential equation problems inside each element, as within generalised Finite Elements [3]. The novelty of the VEM approach is that it avoids computing with the trial virtual functions by basing all computations solely on a set of carefully chosen degrees of freedom. In this way, the VEM achieves flexibility while maintaining the ease of implementation of classical FEMs.
Within this project:
- the VEM framework will be further and developed for the solution of problems driven by application in fluid dynamics and biomedicine,
- the flexibility of the VEM will be exploited for the first time for the design of multiscale approaches and mesh and order adaptive algorithms,
- new public domain software implementing the VEM on general meshes will be published and integrated into the Distributed and Unified Numerics Environment (DUNE).
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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 |
| Summary |
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| Date Materialised |
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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.le.ac.uk |