Inhomogeneous essential boundary conditions can be appended to a well-posed PDE to lead to a combined variational formulation. The domain of the corresponding operator is a Sobolev space on the domain $\Omega$ on which the PDE is posed, whereas the codomain is a Cartesian product of spaces, among them fractional Sobolev spaces of functions on $\partial\Omega$. In this paper, easily implementable minimal residual discretizations are constructed which yield quasi-optimal approximation from the employed trial space, in which the evaluation of fractional Sobolev norms is fully avoided.

翻译：非齐次本质边界条件可以附加到适定偏微分方程上，从而形成组合变分形式。相应算子的定义域是偏微分方程所在区域 $\Omega$ 上的索伯列夫空间，而陪域则是空间的笛卡尔积，其中包括 $\partial\Omega$ 上函数的分数阶索伯列夫空间。本文构建了易于实现的最小残差离散格式，该格式从所用试验空间中获得拟最优逼近，且完全避免了对分数阶索伯列夫范数的计算。