Coupling non-conforming discretizations of PDEs by spectral
approximation of the Lagrange multiplier space
release_jnyc6c7rxbhuhcvao7tvzjfqoq
by
Simone Deparis, Luca Pegolotti
2018
Abstract
This work focuses on the development of a non-conforming domain decomposition
method for the approximation of PDEs based on weakly imposed transmission
conditions: the continuity of the global solution is enforced by a discrete
number of Lagrange multipliers defined over the interfaces of adjacent
subdomains. The method falls into the class of primal hybrid methods, which
also include the well-known mortar method. Differently from the mortar method,
we discretize the space of basis functions on the interface by spectral
approximation independently of the discretization of the two adjacent domains;
one of the possible choices is to approximate the interface variational space
by Fourier basis functions. As we show in the numerical simulations, our
approach is well-suited for the solution of problems with non-conforming meshes
or with finite element basis functions with different polynomial degrees in
each subdomain. Another application of the method that still needs to be
investigated is the coupling of solutions obtained from otherwise incompatible
methods, such as the finite element method, the spectral element method or
isogeometric analysis.
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