We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic partial differential equations. The method is based on techniques from the hybridized discontinuous Galerkin literature where local and global problems are defined for the volume and trace grid points, respectively. By using a Schur complement technique the volume points can be eliminated, which drastically reduces the system size. We derive both the local and global problems, and show that the resulting linear systems are symmetric positive definite. The theoretical stability results are confirmed with numerical experiments as is the accuracy of the method.

我们为二阶线性椭圆型偏微分方程的界面和边界条件强制执行较弱的部分求和有限差分方法提供了一种混合技术。该方法基于混合的不连续Galerkin文献中的技术，其中分别为体积和迹线网格点定义了局部和全局问题。通过使用Schur补码技术，可以消除体积点，从而大大减小了系统尺寸。我们导出了局部和全局问题，并证明了所得线性系统是对称正定的。理论稳定性结果通过数值实验得到了证实，方法的准确性也得到了证实。