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In this paper we show the convergence of a semidiscrete time stepping\theta-scheme on a time grid of variable length to the solution of parabolicoperator differential inclusion in the framework of evolution triple. Themultifunction is assumed to be strong-weak upper-semicontinuous and to havenonempty, closed and convex values, while the quasilinear operator present inthe problem is required to be pseudomonotone, coercive and satisfy theappropriate growth condition. The convergence of piecewise constant andpiecewise linear interpolants constructed on the solutions of time discreteproblems is shown. Under an additional assumption on the sequence of time gridsand regularity of quasilinear operator strong convergence results are obtained.

Semidiscrete variable time-step \theta-scheme for nonmonotone evolution inclusion