Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics

1. Front Matter

   Pages i-vii

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2. Duality Techniques for Error Estimation and Mesh Adaptation in Finite Element Methods

   • Rolf Rannacher

   Pages 1-58

3. Hierarchical Model and Solution Adaptivity of Thin-walled Structures by the Finite-Elements-Method

   • Erwin Stein, Rainer Niekamp, Stephan Ohnimus, Matthias Schimdt

   Pages 59-147

4. Three Lectures on Error Estimation and Adaptivity

   • Peter Hansbo

   Pages 149-193

5. Hierarchic Modelling in Elasticity by generalized p- and hp-FEM

   • C. Schwab

   Pages 195-256

6. Constitutive Relation Error Estimators and Adaptivity in Structural Engineering

   • Pierre Ladevèze

   Pages 257-319

7. Adaptive Methods for Contact Problems

   • Peter Wriggers

   Pages 321-363

This course with 6 lecturers intends to present a systematic survey of recent re­ search results of well-known scientists on error-controlled adaptive finite element methods in solid and structural mechanics with emphasis to problem-dependent concepts for adaptivity, error analysis as well as h- and p-adaptive refinement techniques including meshing and remeshing. Challenging applications are of equal importance, including elastic and elastoplastic deformations of solids, con­ tact problems and thin-walled structures. Some major topics should be pointed out, namely: (i) The growing importance of goal-oriented and local error estimates for quan­ tities of interest—in comparison with global error estimates—based on dual finite element solutions; (a) The importance of the p-version of the finite element method in conjunction with parameter-dependent hierarchical approximations of the mathematical model, for example in boundary layers of elastic plates; (Hi) The choice of problem-oriented error measures in suitable norms, consider­ ing residual, averaging and hierarchical error estimates in conjunction with the efficiency of the associated adaptive computations; (iv) The importance of implicit local postprocessing with enhanced test spaces in order to get constant-free, i. e. absolute-not only relative-discretizati- error estimates; (v) The coupling of error-controlled adaptive discretizations and the mathemat­ ical modeling in related subdomains, such as boundary layers. The main goals of adaptivity are reliability and efficiency, combined with in­ sight and access to controls which are independent of the applied discretization methods. By these efforts, new paradigms in Computational Mechanics should be realized, namely verifications and even validations ofengineering models.

• behavior
• computational mechanics
• control
• elasticity
• finite element method
• mechanics
• model
• modeling
• numerical analysis
• solid
• structural mechanics
• theoretical mechanics

• University of Hannover, Germany

  Erwin Stein

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