Precession is the secular and long-periodic component of the motion of the Earth’s spin axis in the celestial reference frame, approximately exhibiting a motion of about ${50}^{\text{'}\text{'}}$ per year around the pole of the ecliptic. The presently adopted precession model, IAU2006, approximates this motion by polynomial expansions of time that are valid, with very high accuracy, in the immediate vicinity (a few centuries) of the reference epoch J2000.0. For more distant epochs, this approximation however quickly deviates...

We consider a contact problem of planar elastic bodies. We adopt Coulomb friction as (an implicitly defined) constitutive law. We will investigate highly simplified lumped parameter models where the contact boundary consists of just one point. In particular, we consider the relevant static and dynamic problems. We are interested in numerical solution of both problems. Even though the static and dynamic problems are qualitatively different, they can be solved by similar piecewise-smooth continuation...

We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result.

Balancing Domain Decomposition by Constraints (BDDC) belongs to the class of primal substructuring Domain Decomposition (DD) methods. DD methods are iterative methods successfully used in engineering to parallelize solution of large linear systems arising from discretization of second order elliptic problems. Substructuring DD methods represent an important class of DD methods. Their main idea is to divide the underlying domain into nonoverlapping subdomains and solve many relatively small, local...

This study deals with a numerical solution of a 2D flows of a compressible viscous fluids in a convergent channel for low inlet airflow velocity. Three governing systems – Full system, Adiabatic system, Iso-energetic system$basedontheNavier-Stokesequationsforlaminarflowaretested.Thenumericalsolutionisrealizedbyfinitevolumemethodandthepredictor-correctorMacCormackschemewithJamesonartificialviscosityusingagridofquadrilateralcells.TheunsteadygridofquadrilateralcellsisconsideredintheformofconservationlawsusingArbitraryLagrangian-Eulerianmethod.Thenumericalresults,acquiredfromadevelopedprogram,arepresentedforinletvelocity$u=4.12 ms-1$andReynoldsnumberRe=$4 103$.$

A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is tested on a number of problems and numerical results are given.

We present an algorithm for constructing families of conforming (i.e. face-to-face) nonobtuse tetrahedral finite element meshes for convex 3D cylindrical-type domains. In fact, the algorithm produces only path-tetrahedra.

In this work, we present and discuss continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition solved by the finite element and finite difference methods.

In this note, we introduce a new approach to study overlapping domain decomposition methods for optimal control systems governed by partial differential equations. The model considered in our paper is systems governed by wave equations. Our technique could be used for several other equations as well.