Abstract
This paper is mainly concerned with the study of an error estimate of the finite volume approximation to the solution u L (ℝN X ℝ) of the equation u t +div(v f(u)) = 0, where v is a vector function depending on time and space. A “h 1/4” error estimate for an initial value in BV(ℝN) is shown for a large variety of finite volume monotoneous flux schemes, with an explicit or implicit time discretization. For this purpose, the error estimate is given for the general setting of solutions of approximate continuous entropy solutions, where the error is expressed in terms of measures in ℝN X ℝ. All the proofs of this paper can be found in [7].
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Eymard, R., Gallouët, T., Ghilani, M., Herbin, R. (1998). Error Estimate for the Finite Volume Approximate of the Solution to a Nonlinear Convective Equation. In: Crolet, J.M., El. Hatri, M. (eds) Recent Advances in Problems of Flow and Transport in Porous Media. Theory and Applications of Transport in Porous Media, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2856-0_2
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DOI: https://doi.org/10.1007/978-94-017-2856-0_2
Publisher Name: Springer, Dordrecht
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