The finite element method is the most important method for approximating the solution of partial differential equations with applications in solid mechanics, fluid flow, and electromagnetism. The research group has expertise in all aspects of the method: especially analysis of approximation properties; the design and implementation of efficient solution algorithms; and applications of the method to the modelling of physical phenomena. Numerical analysis issues currently being studied include
- efficient mixed approximation methods,
- a posteriori error approximation,
- non-isotropic adaptive refinement,
- adaptive time-stepping.
Some of these aspects are explored in the recently published monograph Finite Elements and Fast Iterative Solvers. The group is also active in writing software, in particular