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首页> 外文期刊>SIAM Journal on Numerical Analysis >A posteriori error estimation based on potential and flux reconstruction for the heat equation
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A posteriori error estimation based on potential and flux reconstruction for the heat equation

机译：基于势和通量重构的热方程后验误差估计

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摘要

We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, various finite volume, and mixed finite element methods in space and the backward Euler scheme in time. Extensions to conforming and nonconforming finite element spatial discretizations are also outlined. Our estimates are based on a H1-conforming reconstruction of the potential, continuous and piecewise affine in time, and a locally conservative H(div)-conforming reconstruction of the flux, piecewise constant in time. They yield a guaranteed and fully computable upper bound on the error measured in the energy norm augmented by a dual norm of the time derivative. Local-in-time lower bounds are also derived; for nonconforming methods on time-varying meshes, the lower bounds require a mild parabolic-type constraint on the meshsize.
机译：我们在统一和完全离散的环境中导出热方程离散化的后验误差估计，包括不连续的Galerkin，各种有限体积和空间上的混合有限元方法以及及时的向后Euler方案。还概述了对符合和不符合的有限元空间离散化的扩展。我们的估计基于电位的H1符合重构，时间上的连续和分段仿射，以及通量的局部保守H（div）符合重构，时间上的分段常数。它们在由时间导数的对偶范数增强的能量范数中测得的误差上产生了有保证且可完全计算的上限。还导出了本地时间下限;对于时变网格上的非协调方法，其下限要求对网格大小有轻微的抛物线型约束。

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