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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)\(\geq 0\) 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

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
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