Error estimation and h-adaptivity for optimal finite element analysis

Adaptive meshing and automatic error control in finite element analysis eliminates the need for re-meshing and re-running design simulations to verify numerical accuracy. The user should only need to enter the component geometry and a coarse finite element mesh. The software autonomously and adaptively refines this mesh where needed. The ideal end result of the simulation is a measurable quantity, calculated to a prescribed error, in less time and less machine memory than if the user applied typical uniform mesh refinement by hand. It would also allow for the simulation of larger objects. The adaptive software package develops a set of refined meshes based on estimates of the error given as an initial solution over a very coarse mesh. These error estimates follow from the Cauchy convergence properties of finite element mathematical analysis. Based on the error estimate generated, the mesh is adaptive refined where needed and the fields are calculated over the new mesh by solution of the sparse matrix equation. This step is repeated until the error in the fields over the mesh is uniform and reduced below a user prescribed level. In general the adaptivity is divided into h-refinement-the breaking of elements into smaller elements as needed, p-enrichment-increasing the order of the element but keeping its size the same, and h-p adaptivity-the combination of the above two techniques.