Abstract
In this essay the rigorous application of the method of vertical lines, i.e. performing the successive steps of spatial and temporal discretization is investigated for dynamical and quasi-statical systems. A particular focus lies in the field of solid mechanics where constitutive models of evolutionary-type are of basic interest. Various coupled systems, i.e. thermo-mechanical, electro-thermal or electro-thermo-mechanical coupled problems are investigated in view of the structure of their resulting equations, commonly, leading to systems of ordinary differential equations or systems of differential-algebraic equations after the spatial discretization step. For the case of a thermo-mechanical and an electro-thermal problem stiffly accurate diagonally-implicit Runge-Kutta methods are applied.
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Hartmann, S., Rothe, S. (2013). A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_10
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