We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is quasi-optimal in two dimensional space and sub-optimal in three dimensional space. Numerical simulations are provided to confirm our findings.

翻译：我们提出一个适应性的有限元素算法,以近似于解决当地界定的、通过正规化(或软体化)近似于其强制力数据的椭圆问题。 我们表明,在二维空间和三维空间,能源误差衰减是近乎最佳的,三维空间是次优的。提供了数字模拟来证实我们的调查结果。