论文标题
拉普拉斯方程的缩放边界有限元法的收敛分析
Convergence analysis of the scaled boundary finite element method for the Laplace equation
论文作者
论文摘要
缩放边界有限元方法（SBFEM）是一种相对较新的边界元素方法，它允许在无需基本解决方案的情况下将解决方案近似为PDE。这里提出了SBFEM收敛分析的理论框架。这是通过定义半分化函数的空间并在该空间上构建插值操作员来实现的。我们证明了此插值操作员的错误估计值，并证明可以在SBFEM中获得最佳收敛到解决方案。这些理论结果得到了数值示例的支持。
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.
