Dawson, C. N.; Russell, T. F.; Wheeler, M. F. Some improved error estimates for the modified method of characteristics. (English) Zbl 0693.65062 SIAM J. Numer. Anal. 26, No. 6, 1487-1512 (1989). A finite element modified method of characteristics (MMOC) for the numerical solution of nonlinear advection-diffuson problems is analyzed. A suboptimal convergence results for the case when the diffusion coefficient D(u)\(\geq 0\) and an \(L^ 2\) error estimate which involves optimal rate and improved norms on the solution are obtained. These results are generalized to the case of a mixed finite element approximation for calculating the pressure, velocity field and MMOC for the concentration field. Reviewer: W.Ames Cited in 72 Documents MSC: 65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations Keywords:error estimates; finite element; method of characteristics; nonlinear advection-diffuson problems; suboptimal convergence; optimal rate PDFBibTeX XMLCite \textit{C. N. Dawson} et al., SIAM J. Numer. Anal. 26, No. 6, 1487--1512 (1989; Zbl 0693.65062) Full Text: DOI Link