Premium
A nonlocal parabolic model for type‐I superconductors
Author(s) -
Slodička Marian,
Van Bockstal Karel
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21880
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , mathematical analysis , kernel (algebra) , type (biology) , convolution (computer science) , boundary value problem , backward euler method , heat kernel , space (punctuation) , euler's formula , boundary (topology) , pure mathematics , euler equations , ecology , linguistics , philosophy , machine learning , artificial neural network , computer science , biology
A vectorial nonlocal linear parabolic problem on a bounded domain with applications in superconductors of type‐I is studied. The nonlocal term is represented by a (space) convolution with a singular kernel (arising in Eringen's model). The well‐posedness of the problem is discussed under low regularity assumptions, and the error estimates for an implicit and semiimplicit time‐discrete scheme (based on backward Euler approximation) are established. It is shown that the solution of the problem satisfies a simpler nonlocal problem with a positive definite kernel if the normal component of the unknown vector field equals zero on the boundary of the domain. Numerical experiments support the obtained theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1821–1853, 2014