Isogeometric mortar methods

• Isogeometric mortar methods from the theoretical and numerical point of view.
• Three well motivated choices of dual spaces with a different degree.
• Two suitable Lagrange multiplier spaces.
• One choice, reasonable at the first glance, but unstable.
• A numerical example coupling non-matching bodies.

The application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically. For the Lagrange multiplier two choices of uniformly stable spaces are presented, both of them are spline spaces but of a different degree. In one case, we consider an equal order pairing for which a cross point modification based on a local degree reduction is required. In the other case, the degree of the dual space is reduced by two compared to the primal. This pairing is proven to be inf–sup stable without any necessary cross point modification. Several numerical examples confirm the theoretical results and illustrate additional aspects.