Bath Numerical Analysis seminar

Inspired by the talk on advanced boundary element methods for the Helmholtz equation, presented by Jon Trevelyan on Monday 7 April, I will present another method for solving Helmholtz equations. I will briefly discuss some ideas from a recent paper by Barnett and Betcke. In the last part of the talk I will try to demonstrate that in the programming language Python we have a tool for numerical computations to rival Matlab.

2008-04-18 no seminar

2008-04-25 no seminar, Landscape talk by Rob Stevenson at 16:15.

2008-05-02 Christopher Baker, On Deterministic and Stochastic Differential Equations with Time Lag,

Christopher Baker (University of Manchester)

http://www.maths.manchester.ac.uk/~cthbaker/

Title : On Deterministic and Stochastic Differential Equations with Time Lag

Abstract :

Many evolutionary problems that are often modelled by ordinary differential equations incorporate a lag in the response to changes that suggests that differential equations with lagging arguments (delay or retarded differential equations) might be more appropriate. We mention application areas and some of the theoretical and numerical approaches to such problems with lagging arguments. We then present, in brief, some results that relate to the numerical treatment of stochastic delay differential equations.

2008-05-09 Ivan Graham, Multiscale Finite Element Methods for High-Contrast Elliptic Interface Problems,

Ivan Graham (University of Bath)

http://www.maths.bath.ac.uk/~igg/

Title : Multiscale Finite Element Methods for High-Contrast Elliptic Interface Problems

2008-05-16 Max Jensen, Miscible Oil Recovery or Non-Conforming Compactness for DG Methods,

Max Jensen (Durham University)

http://www.maths.dur.ac.uk/~dma0mpj/

Title : Miscible Oil Recovery or Non-Conforming Compactness for DG Methods

Abstract :

Miscible displacement methods are increasingly used in oil recovery in order to enhance the production. For instance, currently about 4% of the US total is recovered by means of CO2-based techniques.

In this seminar we examine a mathematical model which represents incompressible, miscible displacement of one fluid by another in a porous medium and its numerical approximation with a combined mixed finite element and discontinuous Galerkin method under minimal regularity assumptions.

The main result is that sequences of discrete solutions weakly accumulate at weak solutions of the continuous problem. In order to deal with the non-conformity of the method and to avoid over-penalisation of jumps across interelement boundaries, the careful construction of a reflexive subspace of the space of bounded variation, which compactly embeds into L^2, and of a lifting operator, which is compatible with the nonlinear diffusion coefficient, are examined. An equivalent skew-symmetric formulation of the convection and reaction terms of the nonlinear partial differential equation allows to avoid flux limitation and nonetheless leads to an unconditionally stable and convergent numerical method.

2008-05-23 Emily Walsh, The Parabolic Monge Ampere Moving Mesh Method,

Emily Walsh (University of Bath)

Title : The Parabolic Monge Ampere Moving Mesh Method

2008-05-30 tba, Unit assessment day

2008-06-20 Clemens Pechstein, FETI Methods for Multiscale Elliptic PDEs and Nonlinear Magnetostatics Problems,

Clemens Pechstein (Johannes Kepler University Linz, Austria)

http://www.numa.uni-linz.ac.at/~clemens/

Title : FETI Methods for Multiscale Elliptic PDEs and Nonlinear Magnetostatics Problems

Abstract : pechstein_bath.pdf

2008-07-04 Sarah Mitchell, Finite-Difference Methods with Increased Accuracy and Correct Initialisation for One-Dimensional Stefan Problems,

Sarah Mitchell (University of Limerick)

http://www.staff.ul.ie/mitchells/index.html http://www.iam.ubc.ca/~sarah/

Title : Finite-Difference Methods with Increased Accuracy and Correct Initialisation for One-Dimensional Stefan Problems

Abstract : SM_abstract.pdf