Three-dimensional mortar finite element method for convection-diffusion equation with nonconforming meshes
In the last decade, non-conforming domain decomposition methods such as the mortar finite element method have been shown to be reliable techniques for several engineering applications that often employ complex finite element design. With this technique, one can conveniently assemble local subcomponents into a global domain without matching the finite element nodes of each subcomponent at the common interface. We employ the mortar finite element formulation in conjunction with higher-order elements, where both mesh refinement and degree enhancement are combined to increase accuracy.
The mortar finite element method has proven to be a good candidate for implementation in two dimensions. In this work, for the first time, we present computational results for the convergence of the mortar finite element technique in three dimensions for the convection-diffusion equation. Our numerical results demonstrate optimality for the resulting non-conforming method for various mesh and polynomial degree discretizations.