A Framework for the Development of Computable Error Bounds for Finite Element Approximations
Seminar Room 1, Newton Institute
We present an overview of our recent work on the development of fully computable upper bounds for the discretisation error measured in the natural (energy) norm for a variety of problems including linear elasticity, convection-diffusion-reaction and Stokes flow in three space dimensions. The upper bounds are genuine upper bounds in the sense that the actual numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem, and are applicable to a variety of discretisation schemes including conforming, non-conforming and discontinuous Galerkin finite element schemes. All constants appearing in the bounds are fully specified. Numerical examples show the estimators are reliable and accurate even in the case of complicated three dimensional problems, and are suitable for driving adaptive finite element solution algorithms.