The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to partial differential equations (PDEs) without the need of a fundamental solution. A theoretical framework for the convergence analysis of SBFEM is proposed here. This is achieved by defining a space of semi-discrete functions and constructing an interpolation operator onto this space. We prove error estimates for this interpolation operator and show that optimal convergence to the solution can be obtained in SBFEM. These theoretical results are backed by two numerical examples.

中文翻译：

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拉普拉斯方程标度边界有限元方法的收敛性分析

比例边界有限元法（SBFEM）是一种相对较新的边界元方法，无需基本解就可以近似求解偏微分方程（PDE）的解。这里提出了SBFEM收敛分析的理论框架。这是通过定义一个半离散函数的空间并在该空间上构造一个插值运算符来实现的。我们证明了该插值算子的误差估计，并表明可以在SBFEM中获得对解的最佳收敛。这些理论结果得到两个数值示例的支持。