论文标题
两场混合的HP-FINITE元素，用于热力学的精制理论中的时间依赖性问题
Two-field mixed hp-finite elements for time-dependent problems in the refined theories of thermodynamics
论文作者
论文摘要
多亏了现代制造技术，具有复杂内部结构（例如泡沫）的异质材料很容易产生。但是，它们的利用并不简单，因为经典的本构法律不一定有效。根据各种实验观察结果，盖尔 - krumhansl方程是建模这种复杂结构的有前途的候选人。但是，实际应用需要一种可靠，有效的算法，该算法能够处理复杂的几何形状和高级热方程式。在本文中，我们介绍了$ hp $ type有限元技术的开发，可以可靠地应用。我们研究了其在各种情况下的收敛性能，与稳定性和快速传播速度的处理方面具有挑战性。该算法也被证明是高效的，比商业算法更快地提供了四个幅度。
Thanks to modern manufacturing technologies, heterogeneous materials with complex inner structures (e.g., foams) can be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not necessarily valid. According to various experimental observations, the Guyer--Krumhansl equation stands as a promising candidate to model such complex structures. However, the practical applications need a reliable and efficient algorithm that is capable of handling both complex geometries and advanced heat equations. In the present paper, we present the development of a $hp$-type finite element technique, which can be reliably applied. We investigate its convergence properties for various situations, being challenging in relation to stability and the treatment of fast propagation speeds. That algorithm is also proved to be outstandingly efficient, providing solutions four magnitudes faster than commercial algorithms.
