The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to 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 a numerical example.

翻译：规模边界限定要素法(SBFEM)是比较近期的边界要素法,它使得在不需要基本解决办法的情况下能够近似解决PDE问题的办法。在此提出了对SBFEM进行趋同分析的理论框架。通过界定半分解功能的空间和在这个空间上建造一个内插操作器来实现这一点。我们证明这个内插操作器的错误估计值,并表明在SBFEM中可以取得与解决办法的最佳趋同。这些理论结果有一个数字例子作为佐证。