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Improved error estimates for mixed finite-element approximations for nonlinear parabolic equations: The continuous-time case. (English) Zbl 0792.65068

Author’s summary: \(L_ 2\)-error estimates are computed for mixed finite- element methods for second-order quasilinear (and linear, variable coefficient) parabolic equations. Results are given for the continuous- time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higher-order spaces.
A second paper [ibid. 10, No. 2, 149-169 (1994; Zbl 0792.65070)] presents the analysis of a fully discrete scheme.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods 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

Citations:

Zbl 0792.65070
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References:

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