A finite element method for elliptic Dirichlet boundary control problems

2018/11/22 by Karkulik, Michael
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1811.09251

Abstract

We consider the finite element discretization of an optimal Dirichlet boundary control problem for the Laplacian, where the control is considered in H^1/2(Γ). To avoid computing the latter norm numerically, we realize it using the H¹(Ω) norm of the harmonic extension of the control. We propose a mixed finite element discretization, where the harmonicity of the solution is included by a Lagrangian multiplier. In the case of convex polygonal domains, optimal error estimates in the H¹ and L² norm are proven. We also consider and analyze the case of control constrained problems.

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