A domain splitting method for heat conduction problems in composite materials
A domain splitting method for heat conduction problems in composite materials
We consider a domain decomposition method for some unsteady heat conduction problem in composite structures. This linear model problem is obtained by homogenization of thin layers of fibres embedded into some standard material. For ease of presentation we consider the case of two space dimensions only. The set of finite element equations obtained by the backward Euler scheme is parallelized in a problem-oriented fashion by some noniterative overlapping domain splitting method, eventually enhanced...
A double -shaped bifurcation curve for a reaction-diffusion model with nonlinear boundary conditions.
A dual mesh method for a nonlocal thermistor problem.
A Fast Iterative Method for Solving Stationary Heat Conduction Problems on Regions Partitioned into Rectangles.
A few results on a class of degenerate parabolic equations
A final value problem for heat equation: regularization by truncation method and new error estimates.
A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition
We deal with a finite difference method for a wide class of nonlinear, in particular strongly nonlinear or quasi-linear, second-order partial differential functional equations of parabolic type with Dirichlet's condition. The functional dependence is of the Volterra type and the right-hand sides of the equations satisfy nonlinear estimates of the generalized Perron type with respect to the functional variable. Under the assumptions adopted, quasi-linear equations are a special case of nonlinear...
A finite difference scheme for a degenerated diffusion equation arising in microbial ecology.
A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation
Skeletal patterning in the vertebrate limb, i.e., the spatiotemporal regulation of cartilage differentiation (chondrogenesis) during embryogenesis and regeneration, is one of the best studied examples of a multicellular developmental process. Recently [Alber et al., The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb, Bulletin of Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation reaction-diffusion system was developed to describe the interaction...
A finite element scheme for the evolution of orientational order in fluid membranes
We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in [J.B. Fournier and P. Galatoa, J. Phys. II7 (1997) 1509–1520; N. Uchida, Phys. Rev. E66 (2002) 040902] which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We introduce...
A finite element solution of the monlinear heat equation
A free boundary problem describing the saturated-unsaturated flow in a porous medium. II: Existence of the free boundary in the 3D case.
A free boundary problem describing the saturated-unsaturated flow in a porous medium.
A free boundary problem for a predator-prey model with nonlinear prey-taxis
This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary...
A free boundary problem for some modified predator-prey model in a higher dimensional environment
We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as goes to infinity and survives in the new environment, or it fails to establish...
A frequency decomposition waveform relaxation algorithm for semilinear evolution equations.
A fundamental estimate and an inequality of Caccioppoli's type for nonlinear parabolic systems of higher order
A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary value problems
A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation
We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the...