TITLE

Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes

AUTHOR(S)
LeFloch, Philippe G.; Okutmustur, Baver; Neves, Wladimir
PUB. DATE
July 2009
SOURCE
Acta Mathematica Sinica;Jul2009, Vol. 25 Issue 7, p1041
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch�s theory which was originally developed in the Euclidian setting. We extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.
ACCESSION #
47488208

 

Related Articles

  • A circular inclusion in a finite domain II. The Neumann-Eshelby problem. Wang, G.; Li, S.; Sauer, R. // Acta Mechanica;Sep2005, Vol. 179 Issue 1/2, p91 

    This is the second paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. In this part, an exact and closed form solution is obtained for the elastic fields of a circular inclusion embedded in a finite circular...

  • On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold. Bernatskaya, J. // Ukrainian Mathematical Journal;Jul2008, Vol. 60 Issue 7, p1028 

    On a Riemannian manifold of nonpositive sectional curvature (Cartan-Hadamard-type manifold), we consider a parabolic equation. The second boundary-value problem for this equation is set in a bounded domain whose surface is a smooth submanifold. We prove that the gradient of the simple-layer...

  • On a class of nonlocal parabolic equations. Bogolyubov, A. N.; Malykh, M. D. // Computational Mathematics & Mathematical Physics;Jun2011, Vol. 51 Issue 6, p987 

    We consider a boundary value problem for parabolic equations with nonlocal nonlinearity of such a form that favorably differs from other equations in that it leads to partial differential equations that have important properties of ordinary differential equations. Local solvability and...

  • POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER. LIU, JIAQUAN; ZENG, PING'AN; XIONG, MING // Chinese Annals of Mathematics;Jul2004, Vol. 25 Issue 3, p383 

    Some results of existence of positive solutions for singular boundary value problems \] \left\{\kern-5pt \begin{array}{ll} -u^{\prime\prime}(t)=p(t)f(u(t))\,,\qquad t\in (0,1), \\[3pt] u(0)=u(1)=0 \end{array}\right. \] are given, where the function p(t) may be singular at t=0,1.

  • A fully nonlinear multi-parameter shell model with thickness variation and a triangular shell finite element. Pimenta, P. M.; Campello, E. M. B.; Wriggers, P. // Computational Mechanics;Aug2004, Vol. 34 Issue 3, p181 

    This work presents a fully nonlinear multi-parameter shell formulation together with a triangular shell finite element for the solution of static boundary value problems. Our approach accounts for thickness variation as additional nodal DOFs, using a director theory with a standard...

  • The First Boundary Value Problem for a Parabolic Equation on a Manifold. Bernatskaya, Yu. // Differential Equations;Jun2005, Vol. 41 Issue 6, p840 

    The article discusses the first boundary value problem for a parabolic equation on a manifold. Parabolic equations with Holder-continuous coefficients in a Euclidean space were comprehensively studied and described in detail in the 1960s in the monographs. The subsequent development of the...

  • Asymptotic boundary conditions for strip-loaded and corrugated surfaces. Kildal, Per-Simon; Kishk, Ahmed; Sipus, Zvonimir // Microwave & Optical Technology Letters;2/5/97, Vol. 14 Issue 2, p99 

    We discuss the unidirectional current screen as an asymptotic strip boundary condition (ASBC) for analysis of field problems containing metal strip grids, and we introduce a related asymptotic corrugation boundary condition (ACBC) for analysis of corrugated surfaces. The boundary conditions are...

  • Effect of boundary conditions on the classical skin depth and nonlocal behavior in inductively coupled plasmas. Aman-ur-Rehman; Yi-Kang Pu // Physics of Plasmas;Sep2005, Vol. 12 Issue 9, p094503 

    When the finiteness of plasma geometry is taken into account, the expression for classical skin depth is different from the one obtained for an unbounded plasma (for both the planar and cylindrical geometries). This change in the expression of the classical skin depth also changes the...

  • Approximation of the Jacobian matrix in ( m, 2)-methods for solving stiff problems. Novikov, E. // Computational Mathematics & Mathematical Physics;Dec2011, Vol. 51 Issue 12, p2065 

    An initial value problem for stiff systems of first-order ordinary differential equations is considered. In the class of ( m, k)-methods, two integration algorithms with a variable step size based on second ( m = k = 2) and third ( k = 2, m = 3) order-accurate schemes are constructed in which...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics