An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix | Zendy

John W. Barrett | Zendy; James F. Blowey | Zendy

Open Access

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix

Author(s) -

John W. Barrett,

James F. Blowey

Publication year - 2001

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/pl00005445

Subject(s) - discretization , mathematics , finite element method , backward euler method , logarithm , matrix (chemical analysis) , piecewise , component (thermodynamics) , limit (mathematics) , piecewise linear function , approximation error , numerical analysis , euler method , mathematical analysis , euler's formula , thermodynamics , physics , materials science , composite material

this paper we consider only the case of a non-degenerate mobilitymatrix L; that is, L min (i) in (1.3b) satisfies the assumption in (D) above. Elliottand Garcke (1997) have proved existence of a solution to (P ` ) and its deep quenchlimit (P) for the physically interesting case of mobility matrices L which degeneratein the pure phases; that is, L min (i) in (1.3b) satisfies L min (i) ? 0 for all i lying inthe interior of the Gibbs simplex Q

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