@article{52233,
  abstract     = {{ELDIRK methods are defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge-Kutta</jats:italic> methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes,  e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability.}},
  author       = {{Mahnken, Rolf and Westermann, Hendrik}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}}},
  doi          = {{10.1007/s00466-024-02442-y}},
  year         = {{2024}},
}

@article{48490,
  abstract     = {{<jats:p>In Nietzsche’s Search for Philosophy – On the Middle Writings, Keith Ansell Pearson directs his interpretive gaze to the middle writings of Nietzsche’s oeuvre, namely Human, All Too Human (HAH), Dawn and The Gay Science (GS). While at least in German Nietzsche scholarship, it is rather debatable whether or not the middle writings should have been considered “neglected”– with perhaps Dawn being a reasonable exception – it is important to read them as more than merely a detour from the “real Nietzsche” found in the Birth of Tragedy and then the late works. While Ansell-Pearson does not presume a homogeneous philosophical approach in the middle works, he characterizes the period as a whole and each work in itself as containing important aspects of Nietzsche’s “search for philosophy”, especially in consideration of Nietzsche’s attempts to “unify thought and life” (4) in what is labelled a “‘philosophical life’” (4).</jats:p>}},
  author       = {{Corall, Niklas}},
  issn         = {{2752-4140}},
  journal      = {{The Agonist}},
  keywords     = {{Ocean Engineering}},
  number       = {{1-2}},
  pages        = {{192--199}},
  publisher    = {{Transnational Press London}},
  title        = {{{Nietzsche’s Search for Philosophy: On the Middle Writings Keith Ansell-Pearson}}},
  doi          = {{10.33182/agon.v13i2.1681}},
  volume       = {{13}},
  year         = {{2023}},
}

@article{45757,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Three prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge–Kutta</jats:italic> (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown.
</jats:p>}},
  author       = {{Mahnken, Rolf}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation}}},
  doi          = {{10.1007/s00466-023-02347-2}},
  year         = {{2023}},
}

@article{30655,
  author       = {{Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  number       = {{3}},
  pages        = {{847--863}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua}}},
  doi          = {{10.1007/s00466-021-02117-y}},
  volume       = {{69}},
  year         = {{2022}},
}

@article{47909,
  author       = {{Reimsbach, Daniel and Hauschild, Bastian}},
  issn         = {{1753-1969}},
  journal      = {{International Journal of Behavioural Accounting and Finance}},
  keywords     = {{Geology, Ocean Engineering, Water Science and Technology}},
  number       = {{1}},
  publisher    = {{Inderscience Publishers}},
  title        = {{{Testing vs. building accounting theory with experimental research: insights from management research}}},
  doi          = {{10.1504/ijbaf.2015.071050}},
  volume       = {{5}},
  year         = {{2015}},
}

@article{45431,
  author       = {{Mahnken, Rolf}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  number       = {{5}},
  pages        = {{408--425}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A Newton-Multigrid algrithm for elasto-plastic/viscoplastic problems}}},
  doi          = {{10.1007/bf00350355}},
  volume       = {{15}},
  year         = {{2008}},
}

@article{45417,
  author       = {{Döbert, C. and Mahnken, Rolf and Stein, E.}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  number       = {{5}},
  pages        = {{456--467}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Numerical simulation of interface debonding with a combined damage/friction constitutive model}}},
  doi          = {{10.1007/s004660050493}},
  volume       = {{25}},
  year         = {{2002}},
}