Fractional operators with inhomogeneous boundary conditions: Analysis, control, and discretization

H Antil, J Pfefferer, S Rogovs - arXiv preprint arXiv:1703.05256, 2017 - arxiv.org
In this paper we introduce new characterizations of spectral fractional Laplacian to
incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical …

Recent advances in finite element methods

S Beuchler, A Rösch - Computational Methods in Applied …, 2023 - degruyter.com
This special issue of Computational Methods in Applied Mathematics is dedicated to
Thomas Apel on the occasion of his 60th birthday in 2022. He was and is a leading figure in …

On discrete shape gradients of boundary type for PDE-constrained shape optimization

W Gong, S Zhu - SIAM Journal on Numerical Analysis, 2021 - SIAM
Shape gradients have been widely used in numerical shape gradient descent algorithms for
shape optimization. The two types of shape gradients, ie, the distributed one and the …

An HDG method for distributed control of convection diffusion PDEs

G Chen, W Hu, J Shen, JR Singler, Y Zhang… - Journal of Computational …, 2018 - Elsevier
We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the
solution of a distributed optimal control problem governed by an elliptic linear convection …

Analysis and approximations of Dirichlet boundary control of Stokes flows in the energy space

W Gong, M Mateos, J Singler, Y Zhang - SIAM Journal on Numerical Analysis, 2022 - SIAM
We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider
cost functionals with two different boundary control regularization terms: the L ^2(Γ)-norm …

A new HDG method for Dirichlet boundary control of convection diffusion PDEs II: Low regularity

W Gong, W Hu, M Mateos, J Singler, X Zhang… - SIAM Journal on …, 2018 - SIAM
In the first part of this work, we analyzed an unconstrained Dirichlet boundary control
problem for an elliptic convection diffusion PDE and proposed a new hybridizable …

A class of embedded DG methods for Dirichlet boundary control of convection diffusion PDEs

G Chen, G Fu, JR Singler, Y Zhang - Journal of Scientific Computing, 2019 - Springer
We investigated a hybridizable discontinuous Galerkin (HDG) method for a convection
diffusion Dirichlet boundary control problem in our earlier work (Gong et al. SIAM J Numer …

A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEs

W Hu, J Shen, JR Singler, Y Zhang, X Zheng - Numerische Mathematik, 2020 - Springer
We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for
approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs …

Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems

W Gong, B Li - IMA Journal of Numerical Analysis, 2020 - academic.oup.com
The parabolic Dirichlet boundary control problem and its finite element discretization are
considered in convex polygonal and polyhedral domains. We improve the existing results on …

An HDG method for Dirichlet boundary control of convection dominated diffusion PDEs

G Chen, JR Singler, Y Zhang - SIAM Journal on Numerical Analysis, 2019 - SIAM
We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the
solution of a convection dominated Dirichlet boundary control problem without constraints …