Multiscale tailored finite point method for second order elliptic equations with rough or highly oscillatory coefficients

We develop a multiscale tailored finite point method (MsTFPM) for second order elliptic equations with rough or highly oscillatory coefficients. The finite point method has been tailored to some particular properties of the problem, so that it can capture the multiscale solutions using coarse meshes without resolving the fine scale structure of the solution. Several numerical examples in oneand two-dimensions are provided to show the accuracy and convergence of the proposed method. In addition, some analysis results based on the maximum principle for the one-dimensional problem are proved. 2 Cross-straits Workshop on Computational Mathematics July 27, 10:30~11:00 Exploring Ground States and Excited States of Spin-1 Bose-Einstein Condensates