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Some improved error estimates for the modified method of characteristics. (English) Zbl 0693.65062
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.
Reviewer: W.Ames

##### MSC:
 65M25 Method of characteristics (IVP of PDE, numerical methods) 65M15 Error bounds (IVP of PDE) 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE) 35K55 Nonlinear parabolic equations
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