Analysis and Approximation of Contact Problems with Adhesion or Damage

Mircea Sofonea, Weimin Han, Meir Shillor

September 26, 2005 by Chapman and Hall/CRC
Reference - 220 Pages
ISBN 9781584885856 - CAT# C5858
Series: Chapman & Hall/CRC Pure and Applied Mathematics


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  • Provides a comprehensive presentation of new dynamic and quasistatic models for contact with adhesion or material damage
  • Presents a systematic development of optimal order error estimates for numerical solutions of the contact problems
  • Demonstrates convergence of the problems with normal compliance to those with the Signorini condition
  • Offers a self-contained presentation of the results
  • Summary

    Research into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor carefully selected several models and thoroughly study them in Analysis and Approximation of Contact Problems with Adhesion or Damage. The book describes very recent models of contact processes with adhesion or damage along with their mathematical formulations, variational analysis, and numerical analysis.

    Following an introduction to modeling and functional and numerical analysis, the book devotes individual chapters to models involving adhesion and material damage, respectively, with each chapter exploring a particular model. For each model, the authors provide a variational formulation and establish the existence and uniqueness of a weak solution. They study a fully discrete approximation scheme that uses the finite element method to discretize the spatial domain and finite differences for the time derivatives. The final chapter summarizes the results, presents bibliographic comments, and considers future directions in the field.

    Employing recent results on elliptic and evolutionary variational inequalities, convex analysis, nonlinear equations with monotone operators, and fixed points of operators, Analysis and Approximation of Contact Problems with Adhesion or Damage places these important tools and results at your fingertips in a unified, accessible reference.