Abstract
SUMMARYIn this paper, the finite volume element method (FVEM) is applied to solve the distributed optimal control problems governed by parabolic equation. We use the method of variational discretization concept to approximate the problems. We consider a semi‐discrete and a fully discrete piecewise linear FVEMs. For the semi‐discrete method, the optimal order error estimates in continuous L ∞ (J; L2) and L ∞ (J; H1)‐norm are obtained; the suboptimal error estimates in continuous L ∞ (J; L ∞ )‐norm are also obtained. For the fully discrete method, the optimal order error estimates in discrete L2(J; L2) and L ∞ (J; L2)‐norm are derived. Numerical experiments are presented to test these theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.
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