All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2

Displaying 21 – 35 of 35

Showing per page

Abstract parabolic problems with non-Lipschitz critical nonlinearities

Konrad J. Wąs (2010)

Colloquium Mathematicae

The Cauchy problem for a semilinear abstract parabolic equation is considered in a fractional power scale associated with a sectorial operator appearing in the linear main part of the equation. Existence of local solutions is proved for non-Lipschitz nonlinearities satisfying a certain critical growth condition.

An Adaptive Multi-level method for Convection Diffusion Problems

Martine Marion, Adeline Mollard (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an a posteriori error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem.

An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection

Josef Dalík, Helena Růžičková (1995)

Applications of Mathematics

We describe a numerical method for the equation u t + p u x - ε u x x = f in ( 0 , 1 ) × ( 0 , T ) with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.

An unconditionally stable finite element scheme for anisotropic curve shortening flow

Klaus Deckelnick, Robert Nürnberg (2023)

Archivum Mathematicum

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method.

Approximation of Parabolic Equations Using the Wasserstein Metric

David Kinderlehrer, Noel J. Walkington (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do not enter into the variational principles, so, for example, discontinuous approximations may be used for approximating the heat equation. We present formulae for computing a Wasserstein metric which enters into the variational...

Asymptotic Behavior of the Solution of the Distribution Diffusion Equation for FENE Dumbbell Polymer Model

I. S. Ciuperca, L. I. Palade (2011)

Mathematical Modelling of Natural Phenomena

This paper deals with the evolution Fokker-Planck-Smoluchowski configurational probability diffusion equation for the FENE dumbbell model in dilute polymer solutions. We prove the exponential convergence in time of the solution of this equation to a corresponding steady-state solution, for arbitrary velocity gradients.

Currently displaying 21 – 35 of 35

Previous Page 2