Error estimates for variational normal derivatives and Dirichlet control\n problems with energy regularization

2018/08/03 by Max Winkler, Winkler, Max · 2 citations
Computer Science · Engineering · #35J05 #49J20 #65N15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1808.01171

openalex publication_date 2018/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article deals with error estimates for the finite element approximation\nof variational normal derivatives and, as a consequence, error estimates for\nthe finite element approximation of Dirichlet boundary control problems with\nenergy regularization. The regularity of the solution is carefully carved out\nexploiting weighted Sobolev and H "older spaces. This allows to derive a sharp\nrelation between the convergence rates for the approximation and the structure\nof the geometry, more precisely, the largest opening angle at the vertices of\npolygonal domains. Numerical experiments confirm that the derived convergence\nrates are sharp.\n

Cited by

• Optimal L² Error Estimates for Non-symmetric Nitsche's Methods
• A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data

Related

• Finite element error estimates for normal derivatives on boundary concentrated meshes
• Analysis and approximations of Dirichlet boundary control of Stokes flows in the energy space
• Regularization and finite element error estimates for elliptic distributed optimal control problems with energy regularization and state or control constraints
• L^∞ norm error estimates for HDG methods applied to the Poisson equation with an application to the Dirichlet boundary control problem
• L²-error estimates for finite element approximations of boundary fluxes