Uniform hp convergence results for the mortar finite element method

The mortar finite element is an example of a non-conforming method which ca n be used to decompose and re-compose a domain into subdomains without requ iring compatibility between the meshes on the separate components. We obtai n stability and convergence results for this method that are uniform in ter ms of both the degree and the mesh used, without assuming quasiuniformity f or the meshes. Our results establish that the method is optimal when non-qu asiuniform h or hp methods are used. Such methods are essential in practice for good rates of convergence when the interface passes through a corner o f the domain. We also give an error estimate for when the p version is used . Numerical results for h,p and hp mortar FEMs show that these methods beha ve as well as conforming FEMs. An hp extension theorem is also proved.