Hybrid high-order methods : a primer with applications to solid mechanics / Matteo Cicuttin, Alexandre Ern, Nicolas Pignet.

Format:

Book

Author/Creator:

Cicuttin, Matteo, author.

Ern, Alexandre, 1967- author.

Pignet, Nicolas, author.

Series:

SpringerBriefs in mathematics.

SpringerBriefs in mathematics

Language:

English

Subjects (All):

Elasticity.

Diffusion--Mathematical models.

Diffusion.

Solid state physics.

Physical Description:

1 online resource (138 pages)

Edition:

1st ed.

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem.

Contents:

Intro

Preface

Contents

1 Getting Started: Linear Diffusion

1.1 Model Problem

1.2 Discrete Setting

1.2.1 The Mesh

1.2.2 Discrete Unknowns

1.3 Local Reconstruction and Stabilization

1.3.1 Local Reconstruction

1.3.2 Local Stabilization

1.3.3 Example: Lowest-Order Case

1.4 Assembly and Static Condensation

1.4.1 The Discrete Problem

1.4.2 Algebraic Realization

1.5 Flux Recovery and Embedding into HDG Methods

1.5.1 Flux Recovery

1.5.2 Embedding into HDG Methods

1.6 One-Dimensional Setting

2 Mathematical Aspects

2.1 Mesh Regularity and Basic Analysis Tools

2.1.1 Mesh Regularity

2.1.2 Functional and Discrete Inverse Inequalities

2.1.3 Polynomial Approximation

2.2 Stability

2.3 Consistency

2.4 H1-Error Estimate

2.5 Improved L2-Error Estimate

3 Some Variants

3.1 Variants on Gradient Reconstruction

3.2 Mixed-Order Variant and Application to Curved Boundaries

3.2.1 Mixed-Order Variant with Higher Cell Degree

3.2.2 Domains with a Curved Boundary

3.3 Finite Element and Virtual Element Viewpoints

4 Linear Elasticity and Hyperelasticity

4.1 Continuum Mechanics

4.1.1 Infinitesimal Deformations and Linear Elasticity

4.1.2 Finite Deformations and Hyperelasticity

4.2 HHO Methods for Linear Elasticity

4.2.1 Discrete Unknowns, Reconstruction, and Stabilization

4.2.2 Discrete Problem, Energy Minimization, and Traction Recovery

4.2.3 Stability and Error Analysis

4.3 HHO Methods for Hyperelasticity

4.3.1 The Stabilized HHO Method

4.3.2 The Unstabilized HHO Method

4.3.3 Nonlinear Solver and Static Condensation

4.4 Numerical Examples

5 Elastodynamics

5.1 Second-Order Formulation in Time

5.1.1 HHO Space Semi-discretization

5.1.2 Time Discretization

5.2 First-Order Formulation in Time

5.2.1 HHO Space Semi-discretization.

5.2.2 Time Discretization

5.3 Numerical Example

6 Contact and Friction

6.1 Model Problem

6.2 HHO-Nitsche Method

6.2.1 FEM-Nitsche Method

6.2.2 Discrete Setting for HHO-Nitsche

6.2.3 Stability and Error Analysis

6.3 Numerical Example

7 Plasticity

7.1 Plasticity Model

7.1.1 Kinematics and Additive Decomposition

7.1.2 Helmholtz Free Energy and Yield Function

7.1.3 Plasticity Problem in Incremental Form

7.2 HHO Discretizations

7.2.1 Discrete Unknowns

7.2.2 Discrete Plasticity Problem in Incremental Form

7.2.3 Nonlinear Solver

7.3 Numerical Examples

7.3.1 Torsion of a Square-Section Bar

7.3.2 Hydraulic Pump Under Internal Forces

8 Implementation Aspects

8.1 Polynomial Spaces

8.2 Algebraic Representation of the HHO Space

8.3 L2-Orthogonal Projections

8.3.1 Quadratures

8.3.2 Reduction Operator

8.4 Algebraic Realization of the Local HHO Operators

8.4.1 Local Reconstruction Operator

8.4.2 The Stabilization Operator

8.5 Assembly and Boundary Conditions

8.6 Remarks on the Computational Cost of HHO Methods

Appendix References.

Notes:

Includes bibliographical references.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Cicuttin, Matteo Hybrid High-Order Methods

ISBN:

3-030-81477-7

OCLC:

1285362184