35 research outputs found
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
Neptune to the Common-wealth of England (1652): the republican Britannia and the continuity of interests
In the seventeenth century, John Kerrigan reminds us, âmodels of empire did not always turn on monarchyâ. In this essay, I trace a vision of âNeptuneâs empireâ shared by royalists and republicans, binding English national interest to British overseas expansion. I take as my text a poem entitled âNeptune to the Common-wealth of Englandâ, prefixed to Marchamont Nedhamâs 1652 English translation of Mare Clausum (1635), John Seldenâs response to Mare Liberum (1609) by Hugo Grotius. This minor work is read alongside some equally obscure and more familiar texts in order to point up the ways in which it speaks to persistent cultural and political interests. I trace the afterlife of this verse, its critical reception and its unique status as a fragment that exemplifies the crossover between colonial republic and imperial monarchy at a crucial moment in British history, a moment that, with Brexit, remains resonant
âNot so much open professed enemies as close hypocritical false-hearted peopleâ: Lucy Hutchinsonâs manuscript account of the services of John Hutchinson and mid-seventeenth-century factionalism
In the 1640s, Lucy Hutchinson (1620-1681) wrote a manuscript account of her husbandâs âservicesâ to the city of Nottingham, a text to which she would return when she came to write the Memoirs of the Life of Colonel John Hutchinson in the 1660s. As well as a detailed description of civil-war Nottinghamshire, this early manuscript traces the factious relationships between the Independent, John Hutchinson, and his fellow Presbyterian committee members from 1641-1645. This factionalism was visible on a national scale in the mid-1640s, as divisions within Parliamentary forces played out in public thanks to the rising popularity of the printed pamphlet. This paper explores the links between Hutchinsonâs seemingly private manuscript account and this burgeoning form of public news
Epicureanism
A brief sketch of the reception of Epicureanism in early modern natural philosophy and metaphysics (15th-18th centuries