We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order convergence for polynomial order up to 3. We show the relation to a Taylor series expansion approach previously used in the context of Nitsche’s method and, in the case of inf-sup stable multiplier methods, prove a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.

中文翻译：

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使用拉格朗日乘子校正狄利克雷边界值

我们提出了一种边界值校正方法，用于曲线边界由直线（平面）近似的情况，并且使用拉格朗日乘子来强制执行狄利克雷边界条件。该方法允许多项式阶数达到 3 的最佳阶数收敛。 我们展示了与之前在 Nitsche 方法上下文中使用的泰勒级数展开方法的关系，并且在 inf-sup 稳定乘法器方法的情况下，证明了先验误差估计明确依赖于网格大小和精确边界和近似边界之间的距离。