A HIGH ORDER ADAPTIVE FINITE ELEMENT METHOD FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS

• 来源期刊: 计算数学（英文版）
• 关键词: Adaptive finite element Nonlinear hyperbolic conservation law
• 年，卷（期）: 2011,（5）
• 页码范围: 491-500
• 页数: 10页
• 语种: 英文
• DOI: 10.4208/jcm.1105-m3392

摘要

In this note,we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations,with the objective of achieving high order accuracy and mesh efficiency.We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem.The computational results verify that,by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al.,an order of N-3/2 accuracy can be obtained when continuous piecewise linear elements are used,where N is the number of elements.