hp‐Discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity
hp‐Discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity
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DOI：
10.1002/fld.271
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发表时间：
2002-09
影响因子：
1.8
通讯作者：
P. Houston;B. Senior;E. Süli
中科院分区：
文献类型：
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作者：
P. Houston;B. Senior;E. Süli
本文对线性和非线性双曲型问题的间断Galerkin有限元法的hp -版进行了后检误差分析。通过采用对偶性参数，对某些实际有用的输出函数导出了明显的后验误差界限。如果原解或对偶解是计算域上的解析函数，这些边界在hp -细化下表现出指数收敛率。基于我们的后验误差界，我们设计并实现了相应的自适应有限元算法，以确保在用户定义的公差范围内可靠有效地控制规定函数的误差。版权所有©2002约翰威利父子有限公司
In this paper we develop the a posteriori error analysis of the hp‐version of the discontinuous Galerkin finite element method for linear and non‐linear hyperbolic problems. By employing a duality argument, sharp a posteriori error bounds are derived for certain output functionals of practical interest. These bounds exhibit an exponential rate of convergence under hp‐refinement if either the primal or the dual solution is an analytic function over the computational domain. Based on our a posteriori error bounds, we design and implement the corresponding hp‐adaptive finite element algorithm to ensure the reliable and efficient control on the error in the prescribed functional to within a user‐defined tolerance. Copyright © 2002 John Wiley & Sons, Ltd.