An improved error bound for reduced basis approximation of linear parabolic problems
An improved error bound for reduced basis approximation of linear parabolic problems
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DOI：
10.1090/s0025-5718-2013-02782-2
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发表时间：
2013-10
期刊：
影响因子：
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通讯作者：
K. Urban;A. Patera
中科院分区：
文献类型：
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作者：
K. Urban;A. Patera
本文考虑线性帕拉型偏微分方程的时空变分形式。我们引入了一个相关联的彼得罗夫-伽辽金真值元离散与有利的离散inf-sup常数，其逆进入误差估计：是统一的热方程;非强制性（但渐近稳定）对流算子仅线性减少的时间。后者反过来又允许减少基近似的有效长时间后验误差界，与经典（悲观）指数增长的能量估计形成鲜明对比。本文对布里埃在（13）中提出的公式作了全面的分析和各种扩展，并给出了一个模型反应-对流-扩散方程的数值结果。
We consider a space-time variational formulation for linear para- bolic partial dierential equations. We introduce an associated Petrov-Galerkin truth nite element discretization with favorable discrete inf-sup constant , the inverse of which enters into error estimates: is unity for the heat equa- tion; decreases only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits eective long-time a posteriori error bounds for reduced basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates. The paper contains a full analysis and various extensions for the formulation introduced briey in (13) as well as numerical results for a model reaction-convection- diusion equation.