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A Time-Fractional Step Method for Conservation Law Related Obstacle Problems

✍ Scribed by Laurent Lévi; Fabrice Peyroutet

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
179 KB
Volume
27
Category
Article
ISSN
0196-8858

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✦ Synopsis

We are interested in approximating the solution of a first-order quasi-linear equation associated with a forced unilateral obstacle condition. With this view, we make use of the time-splitting method developed classically to compute discontinuous solutions of nonhomogeneous scalar conservation laws. Here, one proves that this fractional step method converges in L 1 to the weak entropy solution of the considered obstacle problem. In the case of the Cauchy problem, an L 1 -error bound in √ t is established.

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