Trefftz methods are high-order Galerkin schemes in which all discrete functions are elementwise solution of the PDE to be approximated. They are viable only when the PDE is linear and its coefficients are piecewise constant. We introduce a "quasi-Trefftz" discontinuous Galerkin method for the discretisation of the acoustic wave equation with piecewise-smooth wavespeed: the discrete functions are elementwise approximate PDE solutions. We show that the new discretisation enjoys the same excellent approximation properties as the classical Trefftz one, and prove stability and highorder convergence of the DG scheme. We introduce polynomial basis functions for the new discrete spaces and describe a simple algorithm to compute them. The technique we propose is inspired by the generalised plane waves previously developed for time-harmonic problems with variable coefficients; it turns out that in the case of the time-domain wave equation under consideration the quasi-Trefftz approach allows for polynomial basis functions.

This article analyses the relationship between British fascism and Empire during the interwar period. Based on the premise that historians have neglected the imperial dimension of fascist ideology in interwar Britain, a brief review of existing scholarship will be undertaken before an analysis of fascist ideological conceptions of the British Empire. Looking at the three major fascist parties during the interwar era, the British Fascisti (BF), Imperial Fascist League (IFL) and British Union of Fascists (BUF), it will be demonstrated that whilst unequivocal support for the Empire was a consistent theme throughout fascist rhetoric, individual parties adapted their imperial visions according to their respective ideology. For the BF, the Empire was under constant threat from communist subversion at home and abroad. The IFL looked to demonstrate how international Jewry was attempting to destroy the British Empire. The BUF, developing the most sophisticated ideology and policies relating to Empire, believed a unified ‘organic’ Empire must be consolidated through trade and one ruler if Britain was to remain a global power fit to fight off the pincers of Jewish and communist subversion. This article will conclude by highlighting the need for further enquiry into the relationship between the extreme right and Empire.

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This article examines the relationship between the extreme right and the British Empire during the postwar era. It will first provide a brief review of existing scholarship on the postwar extreme right. It will then go on to argue that scholars have neglected a crucial aspect of the extreme right in postwar Britain -its relationship with imperialism and more specifically, decolonisation -before offering a short overview of extreme right attitudes to Empire during the period in question. The two organisations which will be analysed are Sir Oswald Mosley's Union Movement and the League of Empire Loyalists, led by A. K. Chesterton. The Union Movement sought to break with Britain's imperial past whilst simultaneously promoting a new imperial vision which wanted to see European colonial powers pool their imperial resources in order to match Soviet and US power. The League of Empire Loyalists however sought to promote the conservative tradition of revering the British Empire during its final days and wanted Britain to re-assert control over their imperial possessions. Crucial to both organisations' imperial visions was conspiracy theory, namely, the idea of a global Jewish conspiracy which was seeking to undermine the British Empire. The article will conclude by demonstrating that there is ample opportunity for future study into the relationship between the postwar extreme right and Empire.