1,721,081 research outputs found
On the numerical approach to a two-phase Stefan problem with nonlinear flux
No full textThis paper is devoted to the numerical analysis of a multidimensional two-phase Stefan problem, with a non-linear flux condition on the fixed boundary; the enthalpy formulation is used. A numerical approach suggested by the theory of non-linear semigroup of contractions in L1 (Ω) is introduced; some converging algorithms based on the Crandall-Liggett formula and on the non-linear Chernoff formula are studied. The algebraic non-linear equations are solved by a modified Gauss-Seidel method. The results of several numerical tests are exhibited and discussed
Optimal error estimates for an approximation of degenerate parabolic problems
No full textA fully discrete scheme for a class of multidimensional degenerate parabolic equations is proposed. The discretization is given by C**0 piecewise linear finite elements in space and backward differences in time (the smoothing procedure is avoided). Numerical integration is used; hence the proposed method is easy to implement. Optimal error estimates in energy norms are proved for the solutions
Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter
No full textAn asymptotic analysis is developed, which guarantees that the equation εa(x)∂uε/∂t = ε divx(a(x)▽xuε) - ψ(uε)/2εa(x) in Rn × (0, T), approximates a flow by mean curvature with an error of order O(ε2). The dependence on space of the relaxation parameter εa(x) is crucial for the stability and accuracy of the finite element approximations based on a local mesh refinement strategy. Several numerical experiments simulate the mean curvature motion of various surfaces and confirm the reliability of the asymptotic analysis
Convergence of the approximate free boundary for the multidimensional one-phase Stefan problem
No full textThe variational inequality arising from the one-phase multidimensional Stefan problem is discretized by piecewise-linear finite elements in space and by backward-differences in time. Error estimates for the discrete free boundary at each time-step are proved
Time discretization schemes for the Stefan problem in a concentrated capacity
No full textWe consider two different time discretization algorithms for a nonlinear parabolic PDE arising in heat conduction phenomena with phase changes in two adjoining bodies Ω and Γ, where Γ can be considered as the boundary of Ω. Stability, convergence and error estimate results are given for both algorithms
Numerical analysis of the multidimensional Stefan problem with supercooling and superheating
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