TY - JOUR A1 - Grajewski, Matthias A1 - Hron, Jaroslav A1 - Turek, Stefan T1 - Dual weighted a posteriori error estimation for a new nonconforming linear finite element on quadrilaterals JF - Applied Numerical Mathematics N2 - After a short introduction of a new nonconforming linear finite element on quadrilaterals recently developed by Park, we derive a dual weighted residual-based a posteriori error estimator (in the sense of Becker and Rannacher) for this finite element. By computing a corresponding dual solution we estimate the error with respect to a given target error functional. The reliability and efficiency of this estimator is analyzed in several numerical experiments. Y1 - 2005 U6 - http://dx.doi.org/10.1016/j.apnum.2004.09.016 SN - 0168-9274 VL - 54 IS - 3-4 SP - 504 EP - 518 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Grajewski, Matthias A1 - Hron, Jaroslav A1 - Turek, Stefan T1 - Numerical analysis for a new non-conforming linear finite element on quadrilaterals JF - Journal of Computational and Applied Mathematics Y1 - 2006 U6 - http://dx.doi.org/10.1016/j.cam.2005.05.024 SN - 0377-0427 VL - 193 IS - 1 SP - 38 EP - 50 ER - TY - JOUR A1 - Göddeke, Dominik A1 - Strzodka, Robert A1 - Mohd-Yusof, Jamaludin A1 - McCormick, Patrick A1 - Buijssen, Sven H.M. A1 - Grajewski, Matthias A1 - Turek, Stefan T1 - Exploring weak scalability for FEM calculations on a GPU-enhanced cluster JF - Parallel Computing Y1 - 2007 U6 - http://dx.doi.org/10.1016/j.parco.2007.09.002 SN - 0167-8191 VL - 33 IS - 10-11 SP - 685 EP - 699 ER - TY - JOUR A1 - Grajewski, Matthias A1 - Köster, Michael A1 - Turek, Stefan T1 - Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context JF - SIAM Journal on Scientific Computing Y1 - 2009 U6 - http://dx.doi.org/10.1137/050639387 VL - 31 IS - 2 SP - 1539 EP - 1557 PB - Society for Industrial and Applied Mathematics CY - Philadelphia, Pa. ER - TY - JOUR A1 - Grajewski, Matthias A1 - Köster, Michael A1 - Turek, Stefam T1 - Numerical analysis and implementational aspects of a new multilevel grid deformation method JF - Applied Numerical Mathematics N2 - Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM. Y1 - 2010 U6 - http://dx.doi.org/10.1016/j.apnum.2010.03.017 SN - 0168-9274 VL - 60 IS - 8 SP - 767 EP - 781 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Vögele, Stefan A1 - Rübbelke, Dirk A1 - Govorukha, Kristina A1 - Grajewski, Matthias T1 - Socio-technical scenarios for energy-intensive industries: the future of steel production in Germany JF - Climatic Change Y1 - 2019 U6 - http://dx.doi.org/10.1007/s10584-019-02366-0 SN - 0165-0009 SP - 1 EP - 16 PB - Springer CY - Berlin ER - TY - JOUR A1 - Vögele, Stefan A1 - Grajewski, Matthias A1 - Govorukha, Kristina A1 - Rübbelke, Dirk T1 - Challenges for the European steel industry: Analysis, possible consequences and impacts on sustainable development JF - Applied Energy N2 - The steel industry in the European Union (EU), important for the economy as a whole, faces various challenges. These are inter alia volatile prices for relevant input factors, uncertainties concerning the regulation of CO₂-emissions and market shocks caused by the recently introduced additional import duties in the US, which is an important sales market. We examine primary and secondary effects of these challenges on the steel industry in the EU and their impacts on European and global level. Developing and using a suitable meta-model, we analyze the competitiveness of key steel producing countries with respect to floor prices depending on selected cost factors and draw conclusions on the impacts in the trade of steel on emissions, energy demand, on the involvement of developing countries in the value chain as well on the need for innovations to avoid relocations of production. Hence, our study contributes to the assessment of sustainable industrial development, which is aimed by the Sustainability Development Goal “Build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation countries”. By applying information on country-specific Human Development Indexes (reflecting aspects of life expectancy, education, and per capita income), we show that relocating energy-intensive industries from the EU may not only increase global energy demand and CO₂-emissions, but may also be to the disadvantage of developing countries. Y1 - 2020 U6 - http://dx.doi.org/10.1016/j.apenergy.2020.114633 SN - 0306-2619 VL - 264 IS - Article number: 114633 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Ball, Christopher Stephen A1 - Vögele, Stefan A1 - Grajewski, Matthias A1 - Kuckshinrichs, Wilhelm T1 - E-mobility from a multi-actor point of view: Uncertainties and their impacts JF - Technological Forecasting and Social Change Y1 - 2021 SN - 0040-1625 U6 - http://dx.doi.org/10.1016/j.techfore.2021.120925 VL - 170 IS - Art. 120925 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Rübbelke, Dirk A1 - Vögele, Stefan A1 - Grajewski, Matthias A1 - Zobel, Luzy T1 - Hydrogen-based steel production and global climate protection: An empirical analysis of the potential role of a European cross border adjustment mechanism JF - Journal of Cleaner Production N2 - The European Union's aim to become climate neutral by 2050 necessitates ambitious efforts to reduce carbon emissions. Large reductions can be attained particularly in energy intensive sectors like iron and steel. In order to prevent the relocation of such industries outside the EU in the course of tightening environmental regulations, the establishment of a climate club jointly with other large emitters and alternatively the unilateral implementation of an international cross-border carbon tax mechanism are proposed. This article focuses on the latter option choosing the steel sector as an example. In particular, we investigate the financial conditions under which a European cross border mechanism is capable to protect hydrogen-based steel production routes employed in Europe against more polluting competition from abroad. By using a floor price model, we assess the competitiveness of different steel production routes in selected countries. We evaluate the climate friendliness of steel production on the basis of specific GHG emissions. In addition, we utilize an input-output price model. It enables us to assess impacts of rising cost of steel production on commodities using steel as intermediates. Our results raise concerns that a cross-border tax mechanism will not suffice to bring about competitiveness of hydrogen-based steel production in Europe because the cost tends to remain higher than the cost of steel production in e.g. China. Steel is a classic example for a good used mainly as intermediate for other products. Therefore, a cross-border tax mechanism for steel will increase the price of products produced in the EU that require steel as an input. This can in turn adversely affect competitiveness of these sectors. Hence, the effects of higher steel costs on European exports should be borne in mind and could require the cross-border adjustment mechanism to also subsidize exports. Y1 - 2022 U6 - http://dx.doi.org/10.1016/j.jclepro.2022.135040 SN - 0959-6526 VL - 380 IS - Part 2, Art. Nr.:135040 PB - Elsevier ER - TY - JOUR A1 - Rübbelke, Dirk A1 - Vögele, Stefan A1 - Grajewski, Matthias A1 - Zobel, Luzy T1 - Cross border adjustment mechanism: Initial data for the assessment of hydrogen-based steel production JF - Data in Brief N2 - Ambitious climate targets affect the competitiveness of industries in the international market. To prevent such industries from moving to other countries in the wake of increased climate protection efforts, cost adjustments may become necessary. Their design requires knowledge of country-specific production costs. Here, we present country-specific cost figures for different production routes of steel, paying particular attention to transportation costs. The data can be used in floor price models aiming to assess the competitiveness of different steel production routes in different countries (Rübbelke, 2022). KW - Energy-intensive industry KW - Steel industry KW - Competitiveness KW - Floor prices KW - Cross border adjustment mechanism Y1 - 2023 U6 - http://dx.doi.org/10.1016/j.dib.2023.108907 SN - 2352-3409 VL - 47 IS - Article 108907 SP - 1 EP - 5 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Vögele, Stefan A1 - Josyabhatla, Vishnu Teja A1 - Ball, Christopher A1 - Rhoden, Imke A1 - Grajewski, Matthias A1 - Rübbelke, Dirk A1 - Kuckshinrichs, Wilhelm T1 - Robust assessment of energy scenarios from stakeholders' perspectives JF - Energy N2 - Using scenarios is vital in identifying and specifying measures for successfully transforming the energy system. Such transformations can be particularly challenging and require the support of a broader set of stakeholders. Otherwise, there will be opposition in the form of reluctance to adopt the necessary technologies. Usually, processes for considering stakeholders' perspectives are very time-consuming and costly. In particular, there are uncertainties about how to deal with modifications in the scenarios. In principle, new consulting processes will be required. In our study, we show how multi-criteria decision analysis can be used to analyze stakeholders' attitudes toward transition paths. Since stakeholders differ regarding their preferences and time horizons, we employ a multi-criteria decision analysis approach to identify which stakeholders will support or oppose a transition path. We provide a flexible template for analyzing stakeholder preferences toward transition paths. This flexibility comes from the fact that our multi-criteria decision aid-based approach does not involve intensive empirical work with stakeholders. Instead, it involves subjecting assumptions to robustness analysis, which can help identify options to influence stakeholders' attitudes toward transitions. Y1 - 2023 U6 - http://dx.doi.org/10.1016/j.energy.2023.128326 SN - 1873-6785 (Online) SN - 0360-5442 (Print) IS - In Press, Article 128326 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Grajewski, Matthias A1 - Kleefeld, Andreas T1 - Detecting and approximating decision boundaries in low-dimensional spaces JF - Numerical Algorithms N2 - A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of scattered points along with the corresponding classification algorithm to construct a representation of a decision curve by points with prescribed maximal distance to the true decision curve. Hereby, our algorithm ensures that the representing point set covers the decision curve in its entire extent and features local refinement based on the geometric properties of the decision curve. We demonstrate applications of our method to problems related to the detection of faults, to multi-criteria decision aid and, in combination with Kirsch’s factorization method, to solving an inverse acoustic scattering problem. In all applications we considered in this work, our method requires significantly less pointwise classifications than previously employed algorithms. KW - MCDA KW - Inverse scattering problem KW - Fault approximation KW - Fault detection Y1 - 2023 SN - 1572-9265 N1 - Corresponding author: Matthias Grajewski VL - 93 IS - 4 PB - Springer Science+Business Media CY - Dordrecht ER - TY - JOUR A1 - Rhoden, Imke A1 - Ball, Christopher Stephen A1 - Grajewski, Matthias A1 - Kuckshinrich, Wilhelm T1 - Reverse engineering of stakeholder preferences – A multi-criteria assessment of the German passenger car sector JF - Renewable and Sustainable Energy Reviews N2 - Germany is a frontrunner in setting frameworks for the transition to a low-carbon system. The mobility sector plays a significant role in this shift, affecting different people and groups on multiple levels. Without acceptance from these stakeholders, emission targets are out of reach. This research analyzes how the heterogeneous preferences of various stakeholders align with the transformation of the mobility sector, looking at the extent to which the German transformation paths are supported and where stakeholders are located. Under the research objective of comparing stakeholders' preferences to identify which car segments require additional support for a successful climate transition, a status quo of stakeholders and car performance criteria is the foundation for the analysis. Stakeholders' hidden preferences hinder the derivation of criteria weightings from stakeholders; therefore, a ranking from observed preferences is used. This study's inverse multi-criteria decision analysis means that weightings can be predicted and used together with a recalibrated performance matrix to explore future preferences toward car segments. Results show that stakeholders prefer medium-sized cars, with the trend pointing towards the increased potential for alternative propulsion technologies and electrified vehicles. These insights can guide the improved targeting of policy supporting the energy and mobility transformation. Additionally, the method proposed in this work can fully handle subjective approaches while incorporating a priori information. A software implementation of the proposed method completes this work and is made publicly available. KW - Regionalization KW - Multi-criteria decision analysis KW - Preference assessment KW - E-Mobility KW - Mobility transition Y1 - 2023 U6 - http://dx.doi.org/10.1016/j.rser.2023.113352 SN - 1364-0321 VL - 181 IS - July 2023 SP - Article number: 113352 PB - Elsevier CY - Amsterdam ER -