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The purpose of this paper is to seek to shed light on the practice of incomplete corporate disclosure of quantitative Greenhouse gas (GHG) emissions and investigates whether external stakeholder pressure influences the existence, and separately, the completeness of voluntary GHG emissions disclosures by 431 European companies.

A classification of reporting completeness is developed with respect to the scope, type and reporting boundary of GHG emissions based on the guidelines of the GHG Protocol, Global Reporting Initiative and the Carbon Disclosure Project. Logistic regression analysis is applied to examine whether proxies for exposure to climate change concerns from different stakeholder groups influence the existence and/or completeness of quantitative GHG emissions disclosure.

From 2005 to 2009, on average only 15 percent of companies that disclose GHG emissions report them in a manner that the authors consider complete. Results of regression analyses suggest that external stakeholder pressure is a determinant of the existence but not the completeness of emissions disclosure. Findings are consistent with stakeholder theory arguments that companies respond to external stakeholder pressure to report GHG emissions, but also with legitimacy theory claims that firms can use carbon disclosure, in this case the incomplete reporting of emissions, as a symbolic act to address legitimacy exposures.

Bringing corporate GHG emissions disclosure in line with recommended guidelines will require either more direct stakeholder pressure or, perhaps, a mandated disclosure regime. In the meantime, users of the data will need to carefully consider the relevance of the reported data and develop the necessary competencies to detect and control for its incompleteness. A more troubling concern is that stakeholders may instead grow to accept less than complete disclosure.

The paper represents the first large-scale empirical study into the completeness of companies’ disclosure of quantitative GHG emissions and is the first to analyze these disclosures in the context of stakeholder pressure and its relation to legitimation.

The space discretization of eddy‐current problems in the magnetic vector potential formulation leads to a system of differential‐algebraic equations. They are typically time discretized by an implicit method. This requires the solution of large linear systems in the Newton iterations. The authors seek to speed up this procedure. In most relevant applications, several materials are non‐conducting and behave linearly, e.g. air and insulation materials. The corresponding matrix system parts remain constant but are repeatedly solved during Newton iterations and time‐stepping routines. The paper aims to exploit invariant matrix parts to accelerate the system solution.

Following the principle “reduce, reuse, recycle”, the paper proposes a Schur complement method to precompute a factorization of the linear parts. In 3D models this decomposition requires a regularization in non‐conductive regions. Therefore, the grad‐div regularization is revisited and tailored such that it takes anisotropies into account.

The reduced problem exhibits a decreased effective condition number. Thus, fewer preconditioned conjugate gradient iterations are necessary. Numerical examples show a decrease of the overall simulation time, if the step size is small enough. 3D simulations with large time step sizes might not benefit from this approach, because the better condition does not compensate for the computational costs of the direct solvers used for the Schur complement. The combination of the Schur approach with other more sophisticated preconditioners or multigrid solvers is subject to current research.

The Schur complement method is adapted for the eddy‐current problem. Therefore, a new partitioning approach into linear/non‐linear and static/dynamic domains is proposed. Furthermore, a new variant of the grad‐div gauging is introduced that allows for anisotropies and enables the Schur complement method in 3D.