A Method of Solving the Stability Problem for Complex Matrices.
A method to rigorously enclose eigenpairs of complex interval matrices
In this paper, a rigorous computational method to enclose eigenpairs of complex interval matrices is proposed. Each eigenpair is found by solving a nonlinear equation of the form via a contraction argument. The set-up of the method relies on the notion of , which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
A Metropolis adjusted Nosé-Hoover thermostat
We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nosé-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.
A microbiology application of the skew-Laplace distribution.
Flow cytometry scatter are ofen used in microbiology, and their measures are related to bacteria size and granularity. We present an application of the skew-Laplace distribution to flow cytometry data. The goodness of fit is evaluated both graphically and numerically. We also study skewness and kurtosis values to assess usefulness of the skew-Laplace distribution.
A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion
In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second-order Taylor expansion, where the usual Lévy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds...
A mimetic discretization method for linear elasticity
A Mimetic Discretization method for the linear elasticity problem in mixed weakly symmetric form is developed. The scheme is shown to converge linearly in the mesh size, independently of the incompressibility parameter λ, provided the discrete scalar product satisfies two given conditions. Finally, a family of algebraic scalar products which respect the above conditions is detailed.
A minimum effort optimal control problem for elliptic PDEs
This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation...
A minimum effort optimal control problem for elliptic PDEs
This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation...
A Mixed Finite Element Method Close to the Equilibrium Model.
A mixed finite element method close to the equilibrium model (Preliminary communication)
A mixed finite element method close to the equilibrium model applied to plane elastostatics
A mixed finite element method for a weighted elliptic problem
A mixed finite element method for Darcy flow in fractured porous media with non-matching grids
We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective domains. This is achieved thanks to an enrichment...
A mixed finite element method for Darcy flow in fractured porous media with non-matching grids∗
We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective...
A mixed finite element method for plate bending with a unilateral inner obstacle
A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.
A Mixed Finite Element Method for Solving the Nonstationary Stokes Equation.
A mixed finite element method for the biharmonic problem
A mixed finite element method for the Navier-Stokes equations
A mixed formulation of a sharp interface model of stokes flow with moving contact lines
Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking...