Search results for "Mathematica"
showing 10 items of 7971 documents
Some techniques for improving the resolution of finite difference component-wise WENO schemes for polydisperse sedimentation models
2014
Polydisperse sedimentation models can be described by a system of conservation laws for the concentration of each species of solids. Some of these models, as the Masliyah-Locket-Bassoon model, can be proven to be hyperbolic, but its full characteristic structure cannot be computed in closed form. Component-wise finite difference WENO schemes may be used in these cases, but these schemes suffer from an excessive diffusion and may present spurious oscillations near shocks. In this work we propose to use a flux-splitting that prescribes less numerical viscosity for component-wise finite difference WENO schemes. We compare this technique with others to alleviate the diffusion and oscillatory be…
Parallel finite element splitting-up method for parabolic problems
1991
An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting-up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B-splines. Several numerical examples are presented.
A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm
2014
Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.
On regularity up to the boundary of solutions to a system of degenerate nonlinear elliptic fourth-order equations
2008
Under some hypotheses on weighted functions, using the interior regularity results established in (Kovalevsky, A. and Nicolosi, F., 2005, Existence and regularity of solutions to a system of degenerate nonlinear fourth-order equations. Nonlinear Analysis, 61, 281–307) and estimating the oscillation of solutions near the boundary of Ω, we establish results on regularity up to the boundary of a solutions of the system (1.1).
Implicit–explicit schemes for nonlinear nonlocal equations with a gradient flow structure in one space dimension
2019
A Spline Collocation Scheme for the Spherical Shallow Water Equations
1999
A secular equation for the Jacobian matrix of certain multispecies kinematic flow models
2010
The 1-Harmonic Flow with Values into $\mathbb S^{1}$
2013
We introduce a notion of solution for the $1$-harmonic flow, i.e., the formal gradient flow of the total variation functional with respect to the $L^2$-distance, from a domain of $\mathbb R^m$ into a geodesically convex subset of an $N$-sphere. For such a notion, under homogeneous Neumann boundary conditions, we prove both existence and uniqueness of solutions when the target space is a semicircle and the existence of solutions when the target space is a circle and the initial datum has no jumps of an “angle” larger than $\pi$. Earlier results in [J. W. Barrett, X. Feng, and A. Prohl, SIAM J. Math. Anal., 40 (2008), pp. 1471--1498] and [X. Feng, Calc. Var. Partial Differential Equations, 37…
On the structure of certain ultradistributions
2009
Let "o" be a nonempty open subset of the k-dimensional euclidean space Rk. In this paper we show that, if S is an ultradistribution in "o", belonging to a class of Roumieu type stable under differential operators, then there is a family f , 2 Nk 0, of elements of L1 loc("o") such that S is represented in the formP 2Nk 0 D"a"f "a". Some other results on the structure of certain ultradistributions of Roumieu type are also given.