Thomas Apel

1.6k total citations
51 papers, 1.1k citations indexed

About

Thomas Apel is a scholar working on Computational Mechanics, Mechanics of Materials and Computational Theory and Mathematics. According to data from OpenAlex, Thomas Apel has authored 51 papers receiving a total of 1.1k indexed citations (citations by other indexed papers that have themselves been cited), including 43 papers in Computational Mechanics, 29 papers in Mechanics of Materials and 26 papers in Computational Theory and Mathematics. Recurrent topics in Thomas Apel's work include Advanced Numerical Methods in Computational Mathematics (42 papers), Numerical methods in engineering (28 papers) and Advanced Mathematical Modeling in Engineering (22 papers). Thomas Apel is often cited by papers focused on Advanced Numerical Methods in Computational Mathematics (42 papers), Numerical methods in engineering (28 papers) and Advanced Mathematical Modeling in Engineering (22 papers). Thomas Apel collaborates with scholars based in Germany, France and Austria. Thomas Apel's co-authors include Serge Nicaise, Manfred Dobrowolski, Anna‐Margarete Sändig, Gert Lube, J. R. Whiteman, Joachim Schöberl, Arnd Rösch, Volker Mehrmann, David S. Watkins and S. I. Solov’ev and has published in prestigious journals such as Computer Methods in Applied Mechanics and Engineering, Mathematics of Computation and SIAM Journal on Numerical Analysis.

In The Last Decade

Thomas Apel

48 papers receiving 913 citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Thomas Apel Germany 19 889 551 510 228 205 51 1.1k
Zhong‐Ci Shi China 19 952 1.1× 652 1.2× 404 0.8× 175 0.8× 296 1.4× 75 1.1k
Ricardo G. Durán Argentina 18 991 1.1× 656 1.2× 494 1.0× 142 0.6× 278 1.4× 30 1.2k
So‐Hsiang Chou United States 21 1.3k 1.5× 347 0.6× 304 0.6× 263 1.2× 525 2.6× 52 1.4k
Christian Kreuzer Germany 10 543 0.6× 268 0.5× 352 0.7× 108 0.5× 146 0.7× 19 626
Daniel Peterseim Germany 16 749 0.8× 612 1.1× 661 1.3× 94 0.4× 93 0.5× 64 956
Ricardo G. Durán Argentina 20 835 0.9× 559 1.0× 554 1.1× 172 0.8× 212 1.0× 47 1.2k
Thirupathi Gudi India 17 801 0.9× 533 1.0× 435 0.9× 192 0.8× 194 0.9× 53 911
Alexander Ženíšek Czechia 14 588 0.7× 404 0.7× 375 0.7× 103 0.5× 93 0.5× 42 746
Shipeng Mao China 17 816 0.9× 384 0.7× 278 0.5× 189 0.8× 211 1.0× 81 1.0k
David Mora Chile 15 1.1k 1.2× 740 1.3× 410 0.8× 122 0.5× 405 2.0× 67 1.2k

Countries citing papers authored by Thomas Apel

Since Specialization
Citations

This map shows the geographic impact of Thomas Apel's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Thomas Apel with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Thomas Apel more than expected).

Fields of papers citing papers by Thomas Apel

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Thomas Apel. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Thomas Apel. The network helps show where Thomas Apel may publish in the future.

Co-authorship network of co-authors of Thomas Apel

This figure shows the co-authorship network connecting the top 25 collaborators of Thomas Apel. A scholar is included among the top collaborators of Thomas Apel based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Thomas Apel. Thomas Apel is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Apel, Thomas, et al.. (2024). Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties and graded meshes. Computers & Mathematics with Applications. 175. 236–254.
2.
Apel, Thomas, et al.. (2017). Error estimates for the postprocessing approach applied to Neumann boundary control problems in polyhedral domains. IMA Journal of Numerical Analysis. 38(4). 1984–2025. 3 indexed citations
3.
Apel, Thomas, et al.. (2015). Local mesh refinement for the discretization of Neumann boundary control problems on polyhedra. Mathematical Methods in the Applied Sciences. 39(5). 1206–1232. 8 indexed citations
4.
Apel, Thomas, et al.. (2014). Finite element error estimates on the boundary with application to optimal control. Mathematics of Computation. 84(291). 33–70. 21 indexed citations
5.
Apel, Thomas, et al.. (2012). Crank--Nicolson Schemes for Optimal Control Problems with Evolution Equations. SIAM Journal on Numerical Analysis. 50(3). 1484–1512. 32 indexed citations
6.
Apel, Thomas, et al.. (2011). A Priori Mesh Grading for an Elliptic Problem with Dirac Right-Hand Side. SIAM Journal on Numerical Analysis. 49(3). 992–1005. 36 indexed citations
7.
Apel, Thomas, et al.. (2011). Applications of Mathematics. 5 indexed citations
8.
Apel, Thomas, et al.. (2010). A posteriori error estimation of residual type for anisotropic diffusion–convection–reaction problems. Journal of Computational and Applied Mathematics. 235(8). 2805–2820. 4 indexed citations
9.
Apel, Thomas, et al.. (2008). Edge singularities and structure of the 3-D Williams expansion. Comptes Rendus Mécanique. 336(8). 629–635. 4 indexed citations
10.
Apel, Thomas & Gunter Winkler. (2008). Optimal control under reduced regularity. Applied Numerical Mathematics. 59(9). 2050–2064. 4 indexed citations
11.
Apel, Thomas & Serge Nicaise. (2007). A posteriori error estimations of a SUPG method for anisotropic diffusion–convection–reaction problems. Comptes Rendus Mathématique. 345(11). 657–662. 1 indexed citations
12.
Cucker, Felipe, Ronald DeVore, Herbert Edelsbrunner, et al.. (2004). Foundations of Computational Mathematics, Minneapolis 2002. Cambridge University Press eBooks. 8 indexed citations
13.
Apel, Thomas & Serge Nicaise. (2004). The inf-sup condition for low order elements on anisotropic meshes. CALCOLO. 41(2). 89–113. 3 indexed citations
14.
Apel, Thomas & Serge Nicaise. (2003). The inf-sup condition for the Bernardi-Fortin-Raugel element on anisotropic meshes. Qucosa - Monarch (Chemnitz University of Technology). 1 indexed citations
15.
Apel, Thomas, et al.. (2003). Stability of discretizations of the Stokes problem on anisotropic meshes. Mathematics and Computers in Simulation. 61(3-6). 437–447. 18 indexed citations
16.
Winkler, Gunter, et al.. (2002). Valuation of options in Heston’s stochastic volatility model using finite element methods. 8 indexed citations
17.
Apel, Thomas, Anna‐Margarete Sändig, & S. I. Solov’ev. (2002). Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes. ESAIM Mathematical Modelling and Numerical Analysis. 36(6). 1043–1070. 32 indexed citations
18.
Apel, Thomas & Serge Nicaise. (1998). The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges. Mathematical Methods in the Applied Sciences. 21(6). 519–549. 74 indexed citations
19.
Apel, Thomas & Gert Lube. (1996). Anisotropic Mesh Refinement for Singularly Perturbed Reaction Diffusion Problems. Qucosa - Monarch (Chemnitz University of Technology). 1 indexed citations
20.
Apel, Thomas & Frank Milde. (1996). Comparison of several mesh refinement strategies near edges. Communications in Numerical Methods in Engineering. 12(7). 373–381. 10 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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