A Nitsche-eXtended Finite Element Method for Distributed Optimal Control Problems of Elliptic Interface Equations
2020 ◽
Vol 20
(2)
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pp. 379-393
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Keyword(s):
AbstractThis paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems and apply a Nitsche-eXtended finite element method to discretize the corresponding state and adjoint equations, where piecewise cut basis functions around the interface are enriched into the standard linear element space. Optimal error estimates of the state, co-state and control in a mesh-dependent norm and the {L^{2}} norm are derived. Numerical results are provided to verify the theoretical results.
2009 ◽
Vol 231
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pp. 327-348
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2017 ◽
Vol 55
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pp. 2289-2304
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2015 ◽
Vol 66
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pp. 968-986
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Vol 12
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pp. 727-749
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1995 ◽
Vol 18
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pp. 1036-1043
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2011 ◽
Vol 53
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pp. 375-393
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2016 ◽
Vol 135
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pp. 1121-1170
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