Numerical approximation of internal discontinuity interface problems

Author (s): Discacciati, M.; Quarteroni, A. and Quinodoz, S.
Journal: Journal on Scientific Computing (SIAM)

Volume: 35, Number 3
Pages: 2341 – 2369
Date: 2013

This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain. The interface is characterized via a level set function. The discontinuities are accounted for by using suitable extension operators whose numerical implementation requires a very low computational effort. After carrying out the error analysis, numerical results to validate our approach are presented in one, two, and three dimensions.



@article {DQQ:13,
    AUTHOR = {M. Discacciati and A. Quarteroni and S. Quinodoz},
     TITLE = {Numerical approximation of internal discontinuity interface problems},
   JOURNAL = {SIAM J. Sci. Comput.},
  FJOURNAL = {SIAM Journal on Scientific Computing},
    VOLUME = {35},
      YEAR = {2013},
    NUMBER = {5},
     PAGES = {A2341--A2369},
      ISSN = {1064-8275},
       DOI = {10.1137/110850487},
       URL = {http://dx.doi.org/10.1137/110850487}