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Numerical analysis for a nonlocal phase field system. (English) Zbl 1337.65114

Summary: 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 \(L^\infty \)-norm.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
45K05 Integro-partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
74N99 Phase transformations in solids
80A22 Stefan problems, phase changes, etc.
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