Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys.
Convexity and uniqueness in a free boundary problem arising in combustion theory.
We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω ⊂ QT = Rn x (0,T) for some T > 0 and a function u > 0 in Ω such thatut = Δu, in Ω,u = 0 and |∇u| = 1, on Γ := ∂Ω ∩ QT,u(·,0) = u0, on Ω0,where Ω0 is a given domain in Rn and u0 is a positive and continuous function in Ω0, vanishing on ∂Ω0. If Ω0 is convex and u0 is concave in Ω0, then we show that (u,Ω) is unique and the time sections...
Convexity estimates for nonlinear elliptic equations and application to free boundary problems
Correctors and error estimates in the homogenization of a Mullins–Sekerka problem
Discounted optimal stopping for maxima in diffusion models with finite horizon.
Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation.
Dual finite element analysis for an inequality of the 2nd order
The dual variational formulation of some free boundary value problem is given and its approximation by finite element method is studied, using piecewise linear elements with non-positive divergence.
Dynamic contact problems with given friction for viscoelastic bodies
Embeddedness and uniqueness of minimal surfaces solving a partially free boundary value problem.
Error control and adaptivity for a phase relaxation model
Error Control and Andaptivity for a Phase Relaxation Model
The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori...
Error Estimates for a Semi-Explicit Numerical Scheme for Stefan-Type Problems.
Error estimates for Euler forward scheme related to two-phase Stefan problems
Error estimates of a fully discrete linear approximation scheme for Stefan problem.
Error estimates on homogenization of free boundary velocities in periodic media
Estimation of the conductivity in the one-phase Stefan problem : numerical results
Étude du nombre de solutions pour une classe d'équations elliptiques non-linéaires qui se prolongent en problèmes à frontière libre
Exact solutions for nonclassical Stefan problems.
Existence and approximation results for gradient flows
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Existence and geometric properties of solutions of a free boundary problem in potential theory.