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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: Discrete fractional Sobolev norms with applications

Presented by Daniel Loghin, University of Birmingham

23 January 2009 14:15 in CG60

Fractional Sobolev spaces arise naturally in the formulation of  
many problems of interest, ranging from domain decomposition methods  
to image processing and modeling of complex flows. It is therefore  
desirable to characterise the corresponding discrete spaces with the  
aim to enable new numerical approaches and algorithms. In this work we  
derive discrete norms corresponding to conforming finite element  
discretisations of fractional Sobolev spaces. In particular, we show  
that they involve fractional powers of products of certain Grammian  
matrices associated with the bases of the finite element spaces  
employed. We address the issue of computational complexity of methods  
based on fractional norms by devising a sparse approximation procedure  
based on a generalised Lanczos algorithm. Examples are included in the  
presentation to illustrate the practical implementation of this  

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