Optimal Control Applications and Methods · 2012 · 22 citations · 23 references
ComputingComputational EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsError EstimationFinite Element DiscretizationFinite Element FormulationFinite Volume MethodsA Posteriori Error EstimatesDiscretizationError Estimation For Finite Element SolutionsFinite Element ModelingFinite Element Variational FormulationFinite Volume DiscretizationParabolic Boundary-value Problems
SUMMARY In 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 ; L 2 ) and L ∞ ( J ; H 1 )‐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 L 2 ( J ; L 2 ) and L ∞ ( J ; L 2 )‐norm are derived. Numerical experiments are presented to test these theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.
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