Abstract

In classical finite element and boundary element methods we seek the solution to a boundary-value problem in a space of piecewise polynomial functions. There are some classes of problems for which this approach leads to inefficiencies, sometimes so severe that it becomes infeasible to solve the problem. In these cases, we can make progress by using functions other than the conventional polynomials, the choice of these functions being informed by our knowledge of the form of the solution. In this seminar we will look at the solution to a range of problems in fracture mechanics, wave propagation and heat transfer – each requiring a different enrichment strategy – showing how accurate solutions may be obtained on coarse meshes.

Jon Trevelyan is a Professor of Engineering at Durham University, UK. Following his PhD he worked for 11 years in the commercial software industry in the UK and USA , before returning to academia. Jon’s research involves developing finite element and boundary element methods for classes of problem for which traditional methods become inefficient, inaccurate or impractical. A unifying feature of these works is the use of approximating functions beyond the piecewise polynomials conventionally used in these methods. In 2017 Jon completed his four-year term as Head of Durham’s School of Engineering and Computing Sciences.