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Zbl 0693.65062
Dawson, C.N.; Russell, T.F.; Wheeler, M.F.
Some improved error estimates for the modified method of characteristics. (English)
[J] SIAM J. Numer. Anal. 26, No.6, 1487-1512 (1989). ISSN 0036-1429; ISSN 1095-7170/e

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)$\ge 0$ and an $L\sp 2$ 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.
[W.Ames]

MSC 2000:: *65M25 Method of characteristics (numerical)
65M15 Error bounds (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
35K55 Nonlinear parabolic equations

Keywords: error estimates; finite element; method of characteristics; nonlinear advection-diffuson problems; suboptimal convergence; optimal rate

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