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First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a -point monotone scheme may give an oscillatory solution even though...
First–order accurate monotone conservative schemes have good
convergence and stability properties, and thus play a very
important role in designing modern high resolution shock-capturing
schemes.
Do the monotone difference approximations always
give a good numerical solution in sense of monotonicity preservation
or suppression of oscillations? This note will investigate this problem
from a numerical point of view and show that
a (2K+1)-point monotone scheme may give an oscillatory solution
even...
The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes in , on , . This problem is a particular case of problem (2). Notice that is optimal as coefficient and exponent on the right hand side.
The proof of the Friedrichs' inequality on the class of finite dimensional spaces used in the finite element method is given. In particular, the approximate spaces generated by simplicial isoparametric elements are considered.
We study a model of motion of a passive tracer particle in a turbulent flow that is strongly mixing in time variable. In [8] we have shown that there exists a probability measure equivalent to the underlying physical probability under which the quasi-Lagrangian velocity process, i.e. the velocity of the flow observed from the vintage point of the moving particle, is stationary and ergodic. As a consequence, we proved the existence of the mean of the quasi-Lagrangian velocity, the so-called Stokes...
The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in D.
In this paper we study the behaviour of maximal monotone multivalued highly oscillatory operators. We construct Reuss-Voigt-Wiener and Hashin-Shtrikmann type bounds for the minimal sections of G-limits of multivalued operators by using variational convergence and convex analysis.
In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without
assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and
which include as a particular case, the result of [3].
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