The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution techniques is that discretization only occurs on the boundary, i.e., the complete domain does not need to be discretized. This provides an advantage in terms of time and cost. The algorithm's performance is illustrated through sample test problems with known solutions. A comparison between the exact solution and the BEM numerical solution is done, and error analysis is performed on the results.

翻译：采用分段线性单元的边界元方法（BEM）求解圆盘上拉普拉斯方程二维狄利克雷问题。与许多其他数值解法相比，边界元法的优势在于离散化仅发生在边界上，即无需对整个区域进行离散化。这为计算时间和成本带来了优势。通过已知解的测试算例展示该算法的性能，将精确解与边界元数值解进行对比，并对结果进行误差分析。