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  • 1
    Electronic Resource
    Electronic Resource
    A system of conservation laws including a stiff relaxation term; the 2D case (1996)
    Springer
    BIT 36 (1996), S. 786-813 
    Details
    ISSN: 1572-9125
    Keywords: Hyperbolic conservation laws ; two space dimensions ; relaxation terms ; non-equilibrium ; error estimate ; rate of convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order $$\mathcal{O}(\sqrt {\Delta t} )$$ measured inL 1 is derived. This error bound is independent of the relaxation time δ 〉 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured inL 1 is of order $$\mathcal{O}(\delta ^{1/3} )$$ . Finally, we present some numerical illustrations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01733792
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  • 2
    Electronic Resource
    Electronic Resource
    A numerical comparison of conjugate gradient-like methods (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 793-798 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three second-order, nonselfadjoint partial differential equations in two dimensions are discretized by the finite element method, leading to non-symmetric systems of linear equations. The systems are solved by several conjugate gradient-like methods, and compared for their computational cost. All methods are tested with and without preconditioning.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630040613
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