hp submeshing via non-conforming finite element methods
Padmanabhan Seshaiyer and Manil Suri
Department of Mathematics and Statistics
University of Maryland Baltimore County
Baltimore, MD 21250, USA padhu@math.umbc.edu,
suri@math.umbc.edu
Non-conformity in the $hp$ version can involve incompatibility in both
the degrees and the meshes between adjoining subdomains. In this paper,
we show how the mortar finite element method M0 and two new variants M1,
M2 can be used to join together such incompatible $hp$
sub-discretizations. Our results show optimality of the resulting
non-conforming method for various $h, p$ and $hp$ discretizations,
including the case of exponential $hp$ convergence over geometric meshes.
We also present numerical results for the Lagrange multiplier when the
method is implemented via a mixed method. Three-dimensional
considerations suggest that our methods M1, M2 are easier to generalize
to arbitrary meshes than M0.
