A posteriori error estimation and adaptive meshing using error in constitutive relation

The paper presents a method to control the quality of finite element solutions error in the constitutive relation. An a posteriori estimator is built up. Its construction is general and gives quantitative results about the accuracy of the solution. Both problems of control of quality and mesh optimisation are also discussed. Several examples are presented. A method used to compute a magnetic field that verifies Ampere's law using only local calculations is presented.