TY - JOUR
T1 - Expanded Mixed Finite Element Domain Decomposition Methods on Triangular Grids
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 255
EP - 270
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/524.html
KW - Cell-centered finite difference, domain decomposition, error estimates, fractional step, mixed finite element, operator splitting.
AB - <p style="text-align: justify;">In this work, we present a cell-centered time-splitting technique for solving evolutionary 
diffusion equations on triangular grids. To this end, we consider three variables (namely the
pressure, the flux and a weighted gradient) and construct a so-called expanded mixed finite element 
method. This method introduces a suitable quadrature rule which permits to eliminate both
fluxes and gradients, thus yielding a cell-centered semidiscrete scheme for the pressure with a local
10-point stencil. As for the time integration, we use a domain decomposition operator splitting
based on a partition of unity function. Combining this splitting with a multiterm fractional step
formula, we obtain a collection of uncoupled subdomain problems that can be efficiently solved in
parallel. A priori error estimates for both the semidiscrete and fully discrete schemes are derived
on smooth triangular meshes with six triangles per internal vertex.</p>