We introduce an ultraweak space-time variational formulation for the wave equation, prove
its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability …

In this paper we introduce new characterizations of spectral fractional Laplacian to
incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical …

Abstract Very recently Warma (2019 SIAM J. Control Optim. to appear) has shown that for
nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability …

The paper deals with finite element approximations of elliptic Dirichlet boundary control
problems posed on two-dimensional polygonal domains. Error estimates are derived for the …

A linear quadratic Dirichlet control problem governed by an elliptic equation posed on a
possibly nonconvex polygonal domain is analyzed. Detailed regularity results are provided …

We are interested in acoustic wave propagation in time harmonic regime in a two-
dimensional medium which is a local perturbation of an infinite isotropic or anisotropic …

This paper is concerned with approximations and related discretization error estimates for
the normal derivatives of solutions of linear elliptic partial differential equations. In order to …

This note provides an error estimate for finite element approximation to elliptic partial
differential equations (PDEs) with discontinuous Dirichlet boundary data. Solutions of …

The very weak solution of the Poisson equation with L^2 boundary data is defined by the
method of transposition. The finite element solution with regularized boundary data …

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 …