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A Priori and a Posteriori Error Analysis for a Linear Elliptic Problem with Dynamic Boundary Condition |
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PP: 3305-3317 |
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Author(s) |
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Toufic El Arwadi,
Séréna DIB,
Toni Sayah,
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Abstract |
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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. |
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