Researches on the high-accurate computation and numerical verification for the solution of the partial differential equation with singularity

插值误差的估计在有限元法误差估计中起着至关重要的作用。在我们的研究中，我们得到并证明了三角元上插值误差边界的精确公式。特别地，我们证明了插值误差受三角形的外接圆半径的限制。我们称这个条件为圆半径条件。这一结果使我们能够通过有效的网格划分来计算具有奇异性的偏微分方程的解。

The estimate for the interpolation error plays an essential role in error estimation for Finite Element Method. In our research, we obtained and proved precise formula that bounds interpolation error on the triangular elements. In particular, we proved that the interpolation error is bounded by the radius of circumscribed circle of the triangles. We call this condition circum radius condition. This result enables us to compute solutions of partial differential equation with singularity by efficient mesh division.