Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 2: Adjoint approximations and extensions

Journal article

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882-904] of discrete approximations to the linearized and adjoint equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. We consider a simple modified Lax-Friedrichs discretization on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It...

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Authors: Giles, M; Ulbrich, S

• Journal: SIAM Journal on Numerical Analysis
• Volume: 48
• Issue: 3
• Pages: 905-921
• Publication date: 2010-01-01
• DOI: 10.1137/09078078X
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: Adjoint; Numerical analysis; Conservation law; Hyperbolic; Linearized