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期刊名称: Applications of Mathematics
Volume:52    Issue:3        Page:235-249
ISSN:0862-7940

Two-sided a posteriori error estimates for linear elliptic problems with mixed boundary conditions期刊论文

作者: Korotov Sergey
DOI:10.1007/s10492-007-0012-7

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页码: 235-249
被引频次: 17
出版者: Springer-Verlag,ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS,Springer,Springer Nature B.V
期刊名称: Applications of Mathematics
ISSN: 0862-7940
卷期: Volume:52    Issue:3
语言: English
摘要: The paper is devoted to 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 consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition is considered in this work. On the base of this model, we present simple technologies for straightforward constructing computable upper and lower bounds for the error, which is understood as the difference between the exact solution of the model and its approximation measured in the corresponding energy norm. The estimates obtained are completely independent of the numerical technique used to obtain approximate solutions and are “flexible” in the sense that they can be, in principle, made as close to the true error as the resources of the used computer allow.
相关主题: Mechanics, Fluids, Thermodynamics, a posteriori error estimation, error control in energy norm, Analysis, Mathematical and Computational Physics, differential equation of elliptic type, Appl.Mathematics/Computational Methods of Engineering, Mathematics, two-sided error estimation, Applications of Mathematics, mixed boundary conditions, Optimization, MATHEMATICS, APPLIED, FRACTURE-MECHANICS, Error analysis (Mathematics), Boundary value problems, Studies, Mathematical models,

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