Descrizione

Locally adapted meshes and polynomial degrees can greatly improve
spectral element accuracy and applicability.
A Balancing Domain Decomposition by Constraints (BDDC) preconditioner
is constructed and analyzed for spectral element discretizations with
variable polynomial degree for both continuous and discontinuous
Galerkin discretizations of scalar elliptic problems. The
preconditioner for the discontinuous Galerkin case is reduced to the
continuous case by the Auxiliary Space Method. The proposed BDDC
preconditioner is proven to be scalable in the number of subdomains
and quasi-optimal in both the ratio of local polynomial degree and
element size and the ratio of subdomain and element sizes. Several
numerical experiments in the plane confirm the theoretical convergence
rate estimates obtained and illustrate the preconditioner performance
for both continuous and discontinuous Galerkin discretizations.
Different configurations with locally adapted polynomial degrees are
studied, as well as the preconditioner robustness with respect to
discontinuities of the elliptic coefficients across subdomain
boundaries. 

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