标题： 三维拉普拉斯和赫尔姆霍茨方程曲边界元方法的收敛率 显示英文标题

标题： Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations

摘要： 我们建立了改进的收敛率，用于三维（3D）拉普拉斯和赫姆霍兹方程在光滑几何和数据下的曲边界元方法。 我们的分析依赖于对扰动双线性和共轭双线性形式引入的一致性误差的精确分析。 我们通过基于基函数和四阶曲三角形单元的三维数值实验来说明我们的结果。 显示英文摘要

摘要： We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency errors introduced by the perturbed bilinear and sesquilinear forms. We illustrate our results with numerical experiments in 3D based on basis functions and curved triangular elements up to order four.