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.

在基于非插值函数（即不具有Kroneckerδ属性的函数）的Galerkin型方法的应用中，非均匀Dirichlet（基本）边界条件的施加是一个基本挑战。通常在各种无网格方法以及基于等几何范例的方法中使用此类函数。本文分析了一个模型问题，该模型问题由服从非标准边界条件的泊松方程组成。即，代替经典边界条件，模型问题涉及Dirichlet型和Neumann型非局部边界条件。在基于不均匀有理B样条（NURBS）的等几何框架中的大量数值研究中，得出了具有强和弱强加的不均匀Dirichlet型非局部条件的变分公式，并进行了比较。数值研究中的注意力主要集中在非局部边界条件对所考虑的离散化方法的性质的影响上。