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Volume 1, Issue 1
Numerical Analysis for a Nonlocal Phase Field System

H.T. Banks & J.R. Samuels, Jr.

Int. J. Numer. Anal. Mod. B,1 (2010), pp. 1-29

Published online: 2010-01

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  • Abstract
In this paper, we propose a stable, convergent finite difference scheme to solve numerically a nonlocal phase field system which may model a variety of nonisothermal phase separations in pure materials which can assume two different phases, say solid and liquid, with properties varying in space. The scheme inherits the characteristic property of conservation of internal energy. We also prove that the scheme is uniquely solvable and the numerical solution will approach the true solution in the L^∞-norm.
  • Keywords

Finite difference scheme Nonisothermal Long-range interaction

  • AMS Subject Headings

35k57 34A34 65L12 65N06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-1-1, author = {H.T. Banks and J.R. Samuels, Jr.}, title = {Numerical Analysis for a Nonlocal Phase Field System}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2010}, volume = {1}, number = {1}, pages = {1--29}, abstract = {In this paper, we propose a stable, convergent finite difference scheme to solve numerically a nonlocal phase field system which may model a variety of nonisothermal phase separations in pure materials which can assume two different phases, say solid and liquid, with properties varying in space. The scheme inherits the characteristic property of conservation of internal energy. We also prove that the scheme is uniquely solvable and the numerical solution will approach the true solution in the L^∞-norm.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/322.html} }
TY - JOUR T1 - Numerical Analysis for a Nonlocal Phase Field System AU - H.T. Banks & J.R. Samuels, Jr. JO - International Journal of Numerical Analysis Modeling Series B VL - 1 SP - 1 EP - 29 PY - 2010 DA - 2010/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/322.html KW - Finite difference scheme KW - Nonisothermal KW - Long-range interaction AB - In this paper, we propose a stable, convergent finite difference scheme to solve numerically a nonlocal phase field system which may model a variety of nonisothermal phase separations in pure materials which can assume two different phases, say solid and liquid, with properties varying in space. The scheme inherits the characteristic property of conservation of internal energy. We also prove that the scheme is uniquely solvable and the numerical solution will approach the true solution in the L^∞-norm.
H.T. Banks and J.R. Samuels, Jr.. (2010). Numerical Analysis for a Nonlocal Phase Field System. International Journal of Numerical Analysis Modeling Series B. 1 (1). 1-29. doi:
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