TY - JOUR
T1 - An A-$\phi$ Scheme for Type-II Superconductors
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 - <p style="text-align: justify;">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.</p>