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

Mind, absent characters, and the deployment of ideology in Henry James’s short fiction

This paper examines the role of ideology in the construction of absent characters in Henry James’s short fiction against a methodological background of cognitive narratology and the attendant notions of metarepresentation, extended mind, and distributed identity. Building on the conviction that those minds that communally assemble absent characters by projecting subjective images of them do form identifiable ideological systems rather than arbitrary arrays, an approach to the construction of absent Louisa Brash in “The Beldonald Holbein” (1901) is made in the context of “Daisy Miller” (1878), “The Author of Beltraffio” (1884), and “The Next Time” (1895). Published in three different decades, these stories display absent and quasi‐absent characters who are conjured up for the reader in much the same way as Mrs. Brash is, namely as functions of a priori ideological positions based on sequenced degrees of commitment to the thematic dominant of a tale, a process that often results in deeply conflicted identities.US Fulbright Program/Spanish Ministry of Education, Culture, and Sport, Grant/Award Number: PRX16/00265