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 …
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 …
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
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 …
shape optimization. The two types of shape gradients, ie, the distributed one and the …
An HDG method for distributed control of convection diffusion PDEs
We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the
solution of a distributed optimal control problem governed by an elliptic linear convection …
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
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 …
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
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 …
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
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 …
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
We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for
approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs …
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
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 …
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
We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the
solution of a convection dominated Dirichlet boundary control problem without constraints …
solution of a convection dominated Dirichlet boundary control problem without constraints …