English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this chapter, theoretical and implementation details of the algorithms of hierarchical modeling and hierarchical hp-approximations, residual error estimation methods and four-step adaptive procedures are considered in the context of their application to modeling and simulation of the problems of elasticity, dielectricity and piezoelectricity. In the hierarchical modeling, 3D-based hierarchical elastic and dielectric models are applied. The adaptive discretization process is based on the hierarchical shape functions and the constrained approximations. In the error estimation, the equilibrated residual method is applied, which serves the total and approximation error assessment. These errors control the model and hp-adaptivity. In the case of adaptive algorithms, four-step procedure is utilized. It includes global solutions on the initial mesh, mesh modified in order to remove some undesired numerical phenomena, the intermediate h-refined mesh and the final (or target) p-enriched mesh. Examples demonstrating the effectivity of the mentioned modeling and approximation, error estimation and adaptivity control parts of the overall simulation algorithm in the three classes of problems are presented.

Adaptive Modeling and Simulation of Elastic, Dielectric and Piezoelectric Problems