A deflation formula for tridiagonal matrices
An explicit formula for the deflation of a tridiagonal matrix is presented. The resulting matrix is again tridiagonal.
A derivative array approach for linear second order differential-algebraic systems.
A Derivative-Free Transformation Preserving the Order of Convergence of Iteration Methods in Case of Multiple Zeros.
A descent algorithm for - approximation of continuous functions with values in unitary space
A deterministic discretisation-step upper bound for state estimation via Clark transformations.
A difference method for a nonlinear system of elliptic equations with mixed derivatives
A difference method of solving the differential equation y' = h(t, y, y, y')
A difference scheme for an elliptic system of nonlinear differential-functional equations with Dirichlet type boundary conditions. The existence and uniqueness of solution
A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines
For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present...
A diffusion reaction system modelling spatial patterns
A Direct Algorithm for Optimal Quadratic Splines.
A direct global superconvergence analysis for Sobolev and viscoelasticity type equations
In this paper we study the finite element approximations to the Sobolev and viscoelasticity type equations and present a direct analysis for global superconvergence for these problems, without using Ritz projection or its modified forms.
A Direct Method for Sparse Least Squares Problems with Lower and Upper Bounds.
A direct proof of the equivalence between the entropy solutions of conservation laws and viscosity solutions of Hamilton-Jacobi equations in one-space variable.
A direct solver for finite element matrices requiring memory places
We present a method that in certain sense stores the inverse of the stiffness matrix in memory places, where is the number of degrees of freedom and hence the matrix size. The setup of this storage format requires arithmetic operations. However, once the setup is done, the multiplication of the inverse matrix and a vector can be performed with operations. This approach applies to the first order finite element discretization of linear elliptic and parabolic problems in triangular domains,...
A discrepancy principle for Tikhonov regularization with approximately specified data
Many discrepancy principles are known for choosing the parameter α in the regularized operator equation , , in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and are approximated by Aₙ and respectively with Aₙ not necessarily self-adjoint. This procedure generalizes the work of Engl and Neubauer (1985), and particular cases of the results are applicable...
A discrete contact model for crowd motion
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the...
A discrete contact model for crowd motion
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here...
A discrete kinetic approximation for the incompressible Navier-Stokes equations
In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H-theorem. Numerical tests are performed to investigate their convergence and accuracy.