Mathematical Sciences: Numerical Approximation of Strongly Nonlinear Problems

有了这个奖项，首席研究员将继续他的 研究了相变的数值分析和自由 流体力学和弹性力学中的边界问题。 特别是，他将分析，设计和实现自适应 相场模型的有限元解法 和Cahn-Hilliard方程 将特别强调 在非能量规范的稳定性和误差分析，如 最大限度地规范，并在效率和可靠性的 产生的算法。 自然界中的许多现象都涉及所谓的自由 边界问题，其中很大一部分的解决方案的过程 致力于确定移动边界的位置 两种或两种以上不同的媒介。 一个很好的例子是天气 天气预报或你报纸上的天气图。 这里 气象学家试图预测锋面的速度和位置， 在这种情况下，fronts是用于移动边界的单词 比如说冷空气和暖空气之间的联系 有了这个校长 研究人员将设计数值方法， 由理论导出的一些自由边界问题的解 弹性。 **

With this award the principal investigator will continue his studies into the numerical analysis of phase transitions and free boundary problems that arise in fluid dynamics and elasticity. In particular, he will analyze, design and implement adaptive finite element methods for the solution of the Phase Field Model and the Cahn-Hilliard equation. Special emphasis will be placed upon stability and error analyses in nonenergy norms, such as the maximum norm, and upon the efficiency and reliability of the resulting algorithms. Many phenomena in nature involve what are called free boundary problems, wherein a large part of the solution process is devoted to determining the location of a moving boundary between two or more different media. A good example is a weather forecast or the weather map in your newspaper. Here meteorologists try to predict the speed and location of fronts; in this context fronts are the words used for moving boundaries between warm and cold air, for example. With this the principal investigator will design numerical methods for finding the solution of some free boundary problems that come from the theory of elasticity. **