Progress Report : October 2008 - April 2009

In the first six months of my PhD I have tried to lay a solid foundation in analysis with background reading as well as looking at problems involving finite elements. I hope that this mainly theoretical approach will enable me to produce rigorous results when studying applied problems. More details are included in Section 1. In January I attended the MAGIC Conference in Manchester, where I presented a poster entitled “Finite Element Methods for Flow in Porous Media”. I found this a useful experience that allowed me to meet some other young researchers and discuss my work in an external forum. I found out about this conference through the MAGIC lectures in the past two terms I have attended 4.5 MAGIC lecture courses (as detailed in Section 2). In the Epiphany term I have begun to study some current areas of research, particularly in the area of discontinuous Galerkin methods. I am currently working on an interesting problem trying to produce a combined discontinuous and continuous Galerkin method for the advection-diffusion equation. I present this current work in Section 4 and outline ideas to continue the work in Section 5. Dr. Jensen has been very helpful throughout this initial period, offering weekly supervisions and being prepared to answer questions as they arise. I think that we have established a good working relationship.