@Article{IJNAM-11-2,
author = {},
title = {Expanded Mixed Finite Element Domain Decomposition Methods on Triangular Grids},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2014},
volume = {11},
number = {2},
pages = {255--270},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/2014-IJNAM-524},
url = {https://global-sci.com/article/83337/expanded-mixed-finite-element-domain-decomposition-methods-on-triangular-grids}
}