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We consider, as discretization in space, the nonconforming mesh developed in SUSHI (Scheme Using Stabilization and Hybrid Interfaces) developed in Eymard et al. (2010) for a semi-linear heat equation. The time discretization is performed using a uniform mesh. We are concerned with a nonlinear scheme that has been studied in Bradji (2016) in the context of the general framework GDM (Gradient Discretization Method) (Droniou et al., 2018) which includes SUSHI. We provide sufficient conditions on the size of the spatial mesh and the time step which allow to prove a W1,∞(L2)-error estimate. This error estimate can be viewed as an improvement for the W1,2(L2)-error estimate proved in Bradji (2016). The W1,∞(L2)-error estimate we want to prove in this note was stated without proof in Bradji (2016, Remark 7.2, Page 1302). Its proof is based on a comparison with an appropriately chosen auxiliary finite volume scheme along with the derivation of some new estimates on its solution.

The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.

The authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.

The authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method.

In contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.

The purpose of this study is to examine the effect of foreign direct investment (FDI) on economic growth contingent on the development level of the local financial system in emerging and developing Asia during the period 1996–2017.

The study adopts the threshold approach, namely the panel smooth transition regression (PSTR) model, for the annual data collection of 18 emerging and developing Asian countries in 22 years. The authors analyze the alternative PSTR models on different proxies of financial development (FD).

The results show new findings of two distinct thresholds of FD in the FDI–growth nexus. The growth-enhancing effect of FDI is realized only when the FD lies between the two threshold values. Notably, at very high levels of FD, the beneficial effect of FDI on growth is vanishing.

The authors provide new insights into the growth effect of FDI and the role of FD. The estimated nonlinear effect of FDI on growth and the thresholds of FD can be benchmarks for emerging and developing Asia in assessment of their situations. The results suggest important implications to the region in setting the long-run policies to boost the effect of FDI on economic growth.

The study assesses the non-linear nexus between fixed broadband and economic growth. The study focuses on data from 33 African countries for the period 2010 to 2020.

The empirical evidence is based on unit root tests, panel smooth transition regression and the generalized method of moments.

The following findings are established in this study. (1) The proportion of the population with access to electricity above and below which the relationship between fixed broadband and economic growth changes in sign is about 60%. (2) Below this threshold, each 1% increase in fixed broadband subscriptions induces a decline in economic growth of about 2.58%. Above the threshold, economic growth would increase by 2.43% when fixed broadband subscriptions increase by 1%. Sensitivity analyses and generalized method of moments (GMM) estimation show that these results are robust.

Due to the coronavirus disease (COVID-19) pandemic, which requires countries to take adequate measures to curb the spread of the pandemic, especially by means of virtual economic activities, any national policy aiming at improving the access of populations to high levels of fixed broadband services should be preceded by the implementation of an electrification program for at least 60% of the total population. Otherwise, providing a good quality internet connection for the benefit of the population would not produce the expected effects on economic growth and would, therefore, be counterproductive.

This study complements the extant literature by providing thresholds at which fixed broadband affects economic growth.

The purpose of this study is to seek to re-examine the threshold effects of public debt on economic growth in Africa.

This study applies panel smooth transition regression approach advanced by González et al. (2017). The method allows for both heterogeneity as well as a smooth change of regression coefficients from one regime to another.

A debt threshold in the range of 62–66% is estimated for the whole sample. Low debt is found to be growth neutral but higher public debt is growth detrimental. For middle-income and resource-intensive countries, a debt threshold in the range of 58–63% is estimated. As part of robustness checks, a dynamic panel threshold model was also applied to deal with the endogeneity of debt, and a much higher debt threshold was estimated, at 74.3%. While low public debt is found to be either growth neutral or growth enhancing, high public debt is consistently detrimental to growth.

The findings of this study show that there is no single debt threshold applicable to all African countries, and confirm that the debt threshold level is sensitive to modeling choices. While further analysis is still needed to suggest a policy, the findings of this study show that high debt is detrimental to growth.

The novelty of this study is twofold. Contrary to previous studies on Africa, this study applies a different estimation technique which allows for heterogeneity and a smooth change of regression coefficients from one regime to another. Another novelty distinct from the previous studies is that, for robustness checks, this study divides the sample into low- and middle-income countries, and into resource- and nonresource intensive countries, as debt experience can differ among country groups. Further, as part of robustness checks, another estimation method is also applied in which the threshold variable (debt) is allowed to be endogenous.