Composite mesh concept based FEM error estimation and solution improvement

Abstract

The use of composite finite element models where meshes with different granularities are allowed to share the same problem domain, is introduced. The idea of this method was taken from the mixture theory of multiphase materials, where the properties of each component enter into the formulation affected by a participation factor. The different behaviors of each component mesh due to differences in the model accuracy rather than to the material properties. We perform estimation of local and global errors for some problems in planar domains that are drawn from engineering problems (structural elastic deformations or heat and mass transfer in catalytic chemical reactors). The main examples in this work are elliptic problems with boundary conditions of Dirichlet, Neumann, and mixed types. The method is not restricted to 2D, being also applicable to 3D problems. In this paper, we also develop the use of composite models with the target of improving the numerical solution of finite element models. By using extrapolation-like concepts, improved solutions may be obtained without increasing the computational cost of the problem or requiring postprocessing of the results. Some examples are shown for which exact solution is available in order to validate the method.