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Volume 11, Issue 4
Numerical Schemes for Multi Phase Quadrature Domains

F. Bozorgnia & M. Bazarganzadeh

Int. J. Numer. Anal. Mod., 11 (2014), pp. 726-744.

Published online: 2014-11

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  • Abstract

In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the numerical implementation of the resulting approach and present computational tests.

  • Keywords

Quadrature domain, Free boundary problem, Finite difference method, Degenerate elliptic equation.

  • AMS Subject Headings

35J70, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-726, author = {F. Bozorgnia and M. Bazarganzadeh}, title = {Numerical Schemes for Multi Phase Quadrature Domains}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {4}, pages = {726--744}, abstract = {

In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the numerical implementation of the resulting approach and present computational tests.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/549.html} }
TY - JOUR T1 - Numerical Schemes for Multi Phase Quadrature Domains AU - F. Bozorgnia & M. Bazarganzadeh JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 726 EP - 744 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/549.html KW - Quadrature domain, Free boundary problem, Finite difference method, Degenerate elliptic equation. AB -

In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the numerical implementation of the resulting approach and present computational tests.

F. Bozorgnia and M. Bazarganzadeh. (2014). Numerical Schemes for Multi Phase Quadrature Domains. International Journal of Numerical Analysis and Modeling. 11 (4). 726-744. doi:
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