  The imposition of inhomogeneous Dirichlet (essential) boundary conditions is
a fundamental challenge in the application of Galerkin-type methods based on
non-interpolatory functions, i.e., functions which do not possess the Kronecker
delta property. Such functions typically are used in various meshfree methods,
as well as methods based on the isogeometric paradigm. The present paper
analyses a model problem consisting of the Poisson equation subject to
non-standard boundary conditions. Namely, instead of classical boundary
conditions, the model problem involves Dirichlet- and Neumann-type nonlocal
boundary conditions. Variational formulations with strongly and weakly imposed
inhomogeneous Dirichlet-type nonlocal conditions are derived and compared
within an extensive numerical study in the isogeometric framework based on
non-uniform rational B-splines (NURBS). The attention in the numerical study is
paid mainly to the influence of the nonlocal boundary conditions on the
properties of the considered discretisation methods.

Numerical Analysis;Numerical Analysis