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Partition of Unity Methods
book

Partition of Unity Methods

by Stéphane P. A. Bordas, Alexander Menk, Sundararajan Natarajan
October 2023
Intermediate to advanced content levelIntermediate to advanced
368 pages
12h 57m
English
Wiley
Content preview from Partition of Unity Methods

2 A Step-by-Step Introduction to Enrichment

Stéphane P. A. Bordas1, Alexander Menk2, and Sundararajan Natarajan3

1 University of Luxembourg, Luxembourg, UK2 Robert Bosch GmbH, Germany3 Indian Institute of Technology Madras, India

In the previous chapter, we discussed the approximation properties of the finite element method (FEM) and learnt that it is not ideally suited to treat problems involving “rough” solutions. This happens when the solution or its derivatives are of low-order continuity. Examples of problems with rough solutions include:

  • partial differential equations (PDEs) with discontinuous coefficients (e.g., diffusion in multi-material domains, material interfaces, cracks, shocks, boundary layers, etc.);
  • problems with singular solutions or steep gradients (e.g., cracks in linear elasticity, flow around obstacles, etc.).

We will require the following definitions.

From simple examples where the standard FEM is unable to reproduce certain features ...

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Publisher Resources

ISBN: 9780470667088Purchase Link