MultiMesh Finite Element Methods II: Analysis

We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in arXiv:1803.08741, enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the componen{}ts of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. In the present paper, we prove optimal order emph{a~priori} error estimate as well as optimal order estimates of the condition number.