The Galerkin gradient least-squares method
Computer Methods in Applied Mechanics and Engineering
Adaptive finite element methods for parabolic problems. I.: a linear model problem
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Adaptive finite element methods for parabolic problems IV: nonlinear problems
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Fundamentals of Heat and Mass Transfer
Fundamentals of Heat and Mass Transfer
LabVIEW based Advanced Instrumentation Systems
LabVIEW based Advanced Instrumentation Systems
Unconditional convergence of DIRK schemes applied to dissipative evolution equations
Applied Numerical Mathematics
A time-adaptive fluid-structure interaction method for thermal coupling
Computing and Visualization in Science
Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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An accurate prediction of the temperature distribution in space and time plays an important role in many industrial applications, in particular when phase transformations are involved. In this article the thermo-physical properties of steel 51CrV4 (SAE 6150) are determined and used in numerical simulations. For the simulation of the temperature field a semi-discrete approach is used, consisting of a finite element approximation in space and a high order Runge--- Kutta integration in time. Several adaptive high-order time integration method (stiffly accurate diagonally implicit Runge---Kutta methods) are applied and their computational efficiency is investigated. The theoretical rates of convergence are achieved for all problems, including the non-linear case. Whereas the second order accurate method of Ellsiepen with time adaptive step-size control proves to be most efficient. Further, the influence of the material model on the simulation results is studied and the numerical results are verified by experiments. The best correlation of the simulation and experimental data is achieved using temperature-dependent parameters.