Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Small states, great power? Gaining influence through intrinsic, derivative, and collective power

In recent years, scholars have devoted increased attention to the agency of small states in International Relations. However, the conventional wisdom remains that while not completely powerful, small states are unlikely to achieve much of significance when faced by great power opposition. This argument, however, implicitly rests on resource-based and compulsory understandings of power. This article explores the implicit connections between the concept of "small state" and diverse concepts of power, asking how we should understand these states' attempts to gain influence and achieve their international political objectives. By connecting the study of small states with additional understandings of power, the article elaborates the broader avenues for influence that are open to many states but are particularly relevant for small states. The article argues that small states' power can be best understood as originating in three categories: “derivative,” collective, and particular-intrinsic. Derivative power, coined by Michael Handel, relies upon the relationship with a great power. Collective power involves building coalitions of supportive states, often through institutions. Particular-intrinsic power relies on the assets of the small state trying to do the influencing. Small states specialize in the bases and means of these types of power, which may have unconventional compulsory, institutional, structural, and productive aspects.