A new multiscale finite element method with locally adaptive bubble function enrichment for convective-diffusive-reactive problems

• Main Authors: Syuan-You Su, 蘇宣佑
• Other Authors: Feng-Nan Hwang
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/4fyvp8

碩士 === 國立中央大學 === 數學系 === 106 === In this thesis, we propose an improved method for multiscale finite element method with adaptive bubble enrichment method (MsFEM\_bub). We expected to use less computation cost to get the similar accuracy as the original numerical method. We would show and compare the numerical solutions by simulating the convection-diffusion-reaction problems. \\ We found that the coarse-grid elements that really need to update, no matter multiscale basis functions or bubble functions, are usually at the sharp place of the numerical solutions, and those coarse-grid elements which are at the smooth place, or a small change of the solution before and after update, do not need to update, but MsFEM\_bub will update all the coarse-grid elements, which would cause the waste of computation costs. So according to this idea, we propose multiscale finite element with local adaptive bubble function enhancement, only update the coarse-grid elements for those really need, and do not update for the others not need. After the experiment, we found that through this method, we can reduce the computation costs and get the similar numerical solutions as MsFEM\_bub.