Superconvergent error estimates for a class of discretization methods for a coupled first-order system with discontinuous coefficients

✍ Scribed by Richard E. Ewing; Jian Shen

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 363 KB
• Volume: 15
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199905)15:3<267::aid-num1>3.0.co;2-0

✦ Synopsis

Lithological discontinuities in a reservoir generate discontinuous coefficients for the first-order system of equations used in the simulation of fluid flow in porous media. Systems of conservation laws with discontinuous coefficients also arise in many other physical applications. In this article, we present a class of discretization schemes that include variants of mixed finite element methods, finite volume element methods, and cell-centered finite difference equations as special cases. Error estimates of the order O(h 2 ) in certain discrete L 2 -norms are established for both the primary independent variable and its flux, even in the presence of discontinuous coefficients in the flux term.