We apply the nonconforming discretisation of Wu and Xu (2019) to the tri-Helmholtz equation on the plane where the source term is a functional evaluating the test function on a one-dimensional mesh-aligned embedded curve. We present error analysis for the convergence of the discretisation and linear convergence as a function of mesh size is recovered almost everywhere away from the embedded curve which aligns with classic regularity theory.

翻译：我们将Wu和Xu(2019年)的不兼容分解应用到平面上的三-Helmholtz方程式,在平面上,源术语是功能性评估单维网状嵌入曲线上的测试函数。我们为离异和线性趋同的趋同提供了错误分析,作为网状大小的函数,几乎从符合经典常态理论的嵌入曲线的每个角落都回收出来。