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首页> 外文期刊>Applications of Mathematics >SHARP UPPER GLOBAL A POSTERIORI ERROR ESTIMATES FOR NONLINEAR ELLIPTIC VARIATIONAL PROBLEMS
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SHARP UPPER GLOBAL A POSTERIORI ERROR ESTIMATES FOR NONLINEAR ELLIPTIC VARIATIONAL PROBLEMS

机译：非线性椭圆变分问题的向上全局全局误差估计

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摘要

The paper is devoted to the problem of verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model embracing nonlinear elliptic variational problems is considered in this work. Based on functional type estimates developed on an abstract level, we present a general technology for constructing computable sharp upper bounds for the global error for various particular classes of elliptic problems. Here the global error is understood as a suitable energy type difference between the true and computed solutions. The estimates obtained are completely independent of the numerical technique used to obtain approximate solutions, and are sharp in the sense that they can be, in principle, made as close to the true error as resources of the used computer allow. The latter can be achieved by suitably tuning the auxiliary parameter functions, involved in the proposed upper error bounds, in the course of the calculations.
机译：本文致力于验证在计算机仿真中获得的近似解的准确性问题。此问题与后验误差估计密切相关，为计算误差提供了可计算的界限，并在解决方案域中检测此类误差太大且应执行某些网格细化的区域。这项工作考虑了一个包含非线性椭圆变分问题的数学模型。基于在抽象级别上开发的功能类型估计，我们提出了一种通用技术，可为各种特殊类别的椭圆问题构造全局误差的可计算的清晰上限。此处，全局误差应理解为真实解和计算解之间的适当能量类型差异。所获得的估计值完全独立于用于获得近似解的数值技术，并且在原则上可以使所估计的值尽可能接近所用计算机资源所允许的真实误差。后者可以通过在计算过程中适当地调整建议的上限误差范围内涉及的辅助参数函数来实现。

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