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 Ω on which the PDE is posed, whereas the codomain is a Cartesian product of spaces, among them fractional Sobolev spaces of functions on ∂ Ω \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.

中文翻译：

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在最小残差方法中方便地包含非均匀边界条件

非齐次的基本边界条件可以附加到适定的偏微分方程上，以得到组合的变分公式。相应算子的域是偏微分方程所在域 Ω 上的 Sobolev 空间，而余域是空间的笛卡尔积，其中函数的分数 Sobolev 空间 ∂ Ω \部分\欧米茄 。在本文中，构建了易于实现的最小残差离散化，它从所使用的试验空间中产生准最优近似，其中完全避免了分数 Sobolev 范数的评估。