Verifying Calculations - Forty Years On, 1st ed. 2016 An Overview of Classical Verification Techniques for FEM Simulations SpringerBriefs in Applied Sciences and Technology Series

This work provides an overview of a posteriori error assessment techniques for Finite Element (FE) based numerical models. These tools aim at estimating and controlling the discretization error in scientific computational models, being the basis for the numerical verification of the FE solutions. The text discusses the capabilities and limitations of classical methods to build error estimates which can be used to control the quality of numerical simulations and drive adaptive algorithms, with a focus on Computational Mechanics engineering applications. Fundamentals principles of residual methods, smoothing (recovery) methods, and constitutive relation error (duality based) methods are thus addressed along the manuscript. Attention is paid to recent advances and forthcoming research challenges on related topics.  The book constitutes a useful guide for students, researchers, or engineers wishing to acquire insights into state-of-the-art techniques for numerical verification.

Preface, by Ludovic Chamoin and Pedro Díez.- Explicit Residual Methods, by Yvon Maday.- Residual type error estimators, by Antonio Huerta and Pedro Díez.- Fundaments of recovery-based error estimation and bounding, by E. Nadal and J.J. Ródenas.- The Constitutive Relation Error Method: a general verification tool, by Pierre Ladevèze and Ludovic Chamoin.

The methods are presented in a pedagogically sound way to promote easy learning

Written from the point of view of both engineering and applied mathematics

Illustrated with a wide and relevant set of applications

Includes supplementary material: sn.pub/extras