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Volume 7, Issue 4
An A-$\phi$ Scheme for Type-II Superconductors

Tao Chen, Tong Kang & Jun Li

DOI: 10.4208/eajam.141016.300517a

East Asian J. Appl. Math., 7 (2017), pp. 658-678.

Published online: 2018-02

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  • Abstract

A fully discrete A-$\phi$ finite element scheme for a nonlinear model of type-II superconductors is proposed and analyzed. The nonlinearity is due to a field dependent conductivity with the regularized power-law form. The challenge of this model is the error estimate for the nonlinear term under the time derivative. Applying the backward Euler method in time discretisation, the well-posedness of the approximation problem is given based on the theory of monotone operators. The fully discrete system is derived by standard finite element method. The error estimate is suboptimal in time and space.

  • Keywords

Nonlinearity, finite element methods, well-posedness, convergence, error estimates.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-658, author = {Tao Chen, Tong Kang and Jun Li}, title = {An A-$\phi$ Scheme for Type-II Superconductors}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {4}, pages = {658--678}, abstract = {

A fully discrete A-$\phi$ finite element scheme for a nonlinear model of type-II superconductors is proposed and analyzed. The nonlinearity is due to a field dependent conductivity with the regularized power-law form. The challenge of this model is the error estimate for the nonlinear term under the time derivative. Applying the backward Euler method in time discretisation, the well-posedness of the approximation problem is given based on the theory of monotone operators. The fully discrete system is derived by standard finite element method. The error estimate is suboptimal in time and space.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.141016.300517a}, url = {http://global-sci.org/intro/article_detail/eajam/10712.html} }
TY - JOUR T1 - An A-$\phi$ Scheme for Type-II Superconductors AU - Tao Chen, Tong Kang & Jun Li JO - East Asian Journal on Applied Mathematics VL - 4 SP - 658 EP - 678 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.141016.300517a UR - https://global-sci.org/intro/article_detail/eajam/10712.html KW - Nonlinearity, finite element methods, well-posedness, convergence, error estimates. AB -

A fully discrete A-$\phi$ finite element scheme for a nonlinear model of type-II superconductors is proposed and analyzed. The nonlinearity is due to a field dependent conductivity with the regularized power-law form. The challenge of this model is the error estimate for the nonlinear term under the time derivative. Applying the backward Euler method in time discretisation, the well-posedness of the approximation problem is given based on the theory of monotone operators. The fully discrete system is derived by standard finite element method. The error estimate is suboptimal in time and space.

Tao Chen, Tong Kang and Jun Li. (2018). An A-$\phi$ Scheme for Type-II Superconductors. East Asian Journal on Applied Mathematics. 7 (4). 658-678. doi:10.4208/eajam.141016.300517a
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