Robust DPG Methods for Transient Convection-Diffusion
Robust DPG Methods for Transient Convection-Diffusion
复制标题
用于瞬态对流扩散的鲁棒 DPG 方法
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
L. Demkowicz
中科院分区：
文献类型：
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作者：
Truman Ellis;Jesse Chan;L. Demkowicz
我们介绍了两种求解暂态对流扩散问题的稳健DPG方法。一旦选择了变分公式，测试标准的选择就会对特定DPG方法的质量产生至关重要的影响。期望测试范数以等价于L2的范数产生解的收敛，同时产生可精确计算的最优测试函数，并保持在高度自适应网格上求解的最优测试函数的良好条件性。引入了两个这样的稳健范数，并证明它们保证了主解变量的接近L2收敛。数值实验表明这两种方法具有较强的收敛能力。
We introduce two robust DPG methods for transient convection-diffusion problems. Once a variational formulation is selected, the choice of test norm critically influences the quality of a particular DPG method. It is desirable that a test norm produce convergence of the solution in a norm equivalent to L2 while producing optimal test functions that can be accurately computed and maintaining good conditioning of the optimal test function solve on highly adaptive meshes. Two such robust norms are introduced and proven to guarantee close to L2 convergence of the primary solution variable. Numerical experiments demonstrate robust convergence of the two methods.