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Volume 11, Issue 2
Expanded Mixed Finite Element Domain Decomposition Methods on Triangular Grids

A. Arraras sand L. Portero

Int. J. Numer. Anal. Mod., 11 (2014), pp. 255-270.

Published online: 2014-11

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  • Abstract

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.

  • Keywords

Cell-centered finite difference, domain decomposition, error estimates, fractional step, mixed finite element, operator splitting.

  • AMS Subject Headings

65M06, 65M12, 65M15, 65M20, 65M55, 65M60, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-255, author = {A. Arraras sand L. Portero}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/524.html} }
TY - JOUR T1 - Expanded Mixed Finite Element Domain Decomposition Methods on Triangular Grids AU - A. Arraras sand L. Portero 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 -

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.

A. Arraras sand L. Portero. (2014). Expanded Mixed Finite Element Domain Decomposition Methods on Triangular Grids. International Journal of Numerical Analysis and Modeling. 11 (2). 255-270. doi:
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