Perturbation methods in the theory of heat conduction
Perturbation of mixed variational problems. Application to mixed finite element methods
Perturbation of parallel asynchronous linear iterations by floating point errors.
Perturbation results for nearly uncoupled Markov chains with applications to iterative methods.
Perturbation series and defect correction for the refinement of approximate eigenelements of linear integral operators
Perturbation theorems for the matrix eigenvalue problem
Perturbations numériques des évolutions parabolique et hyperbolique
Perturbations of an Ostrowski type inequality and applications.
Perturbations of Best Approximation Problems.
Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes
Perturbed Collocation and Runge-Kutta Methods.
Perturbed discrete time dynamical systems
Perturbed Newton-like methods and nondifferentiable operator equations on Banach spaces with a convergence structure.
Perturbed three-step approximation process with errors for a generalized implicit nonlinear quasivariational inclusions.
P-Functionale und Randwerte zu Hypoelliptischen Differentialoperatoren.
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...
Phase field model for mode III crack growth in two dimensional elasticity
A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.
Phase portraits of planar vector fields: Computer proofs.
Piecewise bilinear preconditioning of high-order finite element method.