An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDE

We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a \emph{convection dominated} Dirichlet boundary control problem. Dirichlet boundary control problems and convection dominated problems are each very challenging numerically due to solutions with low regularity and sharp layers, respectively. Although there are some numerical analysis works in the literature on \emph{diffusion dominated} convection diffusion Dirichlet boundary control problems, we are not aware of any existing numerical analysis works for convection dominated boundary control problems. Moreover, the existing numerical analysis techniques for convection dominated PDEs are not directly applicable for the Dirichlet boundary control problem because of the low regularity solutions. In this work, we obtain an optimal a priori error estimate for the control under some conditions on the domain and the desired state. We also present some numerical experiments to illustrate the performance of the HDG method for convection dominated Dirichlet boundary control problems

Visualising Surfaces, Surfacing Vision: Introduction

In this Introduction to a special section on Visualising Surfaces, Surfacing Vision, we argue that to conceive vision in the contemporary world it is necessary to examine its embedding within, expression via and organisation on the surface. First, we review recent social and cultural theories to demonstrate how and why an attention to surfaces is salient today. Second, we consider how vision may be understood in terms of surfaces, discussing the emergence of the term ‘surface’, and its transhistorical relationship with vision. Third, we introduce the contributions to the special section, which cover written articles and artworks. We make connections between them, including their exploration of reflexivity and recursion, observation, objectivity and agency, ontology and epistemology, relationality, process, and two- and three-dimensionality. Fourth, we consider some implications of an understanding of visualising surfaces/surfacing vision