@article{oai:toyama.repo.nii.ac.jp:00017105,
 author = {Okumura, Hiroshi},
 issue = {2},
 journal = {富山大学人間発達科学部紀要 = Memoirs of the Faculty of Human Development University of Toyama},
 month = {Mar},
 note = {This paper presents a variational multiscale (VMS) finite element method based on the bubble element, which enables the establishing of a multiscale function to stabilize the advective-diffusive limit and the discontinuity in steady advection-diffusion problems. Furthermore, it is proved that the present VMS method is equivalent to stabilized finite element methods with the space of piecewise linear functions on elements. It is also shown that the present VMS method solves unresolvable scales under the mesh size by the Laplacian of bubble nodal values. This yields some stabilization for linear nodal values. In some numerical experiments, we show L² and H ¹ error norms and the efficiencies of the present VMS method., Article, 富山大学人間発達科学部紀要, 13巻2号, 2019.03.20, Page 297-304},
 pages = {297--304},
 title = {Variational Multiscale Finite Element Method Based on Bubble Element for Steady Advection-Diffusion Equations},
 volume = {13},
 year = {2019}
}