TY - JOUR

T1 - Quasimonotone schemes for scalar conservation laws. Part II

AU - Cockburn, Bernardo

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1990

Y1 - 1990

N2 - In this paper, the technique of construction and analysis of quasimonotone finite-difference numerical schemes for scalar conservation laws in one space dimension, developed in Part I, is extended to a wide class of Petrov-Galerkin finite-element methods. The resulting schemes are called the quasimonotone finite-element schemes. The approximate solution is written as ūh + ūh, where ūh is a piecewise-constant function. The Petrov-Galerkin methods are then considered to be a set of equations that defines 'the parameter' ūh, plus a single equation, which is essentially a finite-difference scheme, that defines 'the means' ūh. All the results of the theory of quasimonotone finite-difference schemes can be carried over this finite-element framework by this simple point of view.

AB - In this paper, the technique of construction and analysis of quasimonotone finite-difference numerical schemes for scalar conservation laws in one space dimension, developed in Part I, is extended to a wide class of Petrov-Galerkin finite-element methods. The resulting schemes are called the quasimonotone finite-element schemes. The approximate solution is written as ūh + ūh, where ūh is a piecewise-constant function. The Petrov-Galerkin methods are then considered to be a set of equations that defines 'the parameter' ūh, plus a single equation, which is essentially a finite-difference scheme, that defines 'the means' ūh. All the results of the theory of quasimonotone finite-difference schemes can be carried over this finite-element framework by this simple point of view.

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U2 - 10.1137/0727017

DO - 10.1137/0727017

M3 - Article

AN - SCOPUS:0025385611

VL - 27

SP - 247

EP - 258

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 1

ER -