Finite element error estimates for a mixed degenerate parabolic model

Finite element error estimates for a mixed degenerate parabolic model

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The aim of this note is to Lift Capacitor deduce error estimates for a fully-discrete finite element method approximation of a kind of degenerate mixed parabolic equations.The obtained results consider regularity assumptions about the main variable according to the degenerate character of the problem, given by the term involving the time-derivative, which is represented with a non-invertible linear operator $R$.We show two different approaches to obtain the error estimates.The first one needs to introduce an extension Sauce Pans operator of $R$ and the second one requires to add a new ellipticity property for this operator.

These error estimates can be applied to analyze the fully-discrete finite element method approximation of an eddy current model.