Applied Mathematics & Information Sciences

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In this paper, we study the time dependent linear elliptic problem with dynamic boundary condition. The problem is discretized by the backward Euler’s scheme in time and finite elements in space. In this work, an optimal a priori error estimate is established and an optimal a posteriori error with two types of computable error indicators is proved. The first one is linked to the time discretization and the second one to the space discretization. Using these a posteriori errors estimates, an adaptive algorithm for computing the solution is proposed. Finally, numerical experiments are presented to show the effectiveness of the obtained error estimators and the proposed adaptive algorithm.