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Hybrid High-Order Method for Polytopal Meshes Design, Analysis, and Applications

Di Pietro Daniele Antonio Droniou, Jérôme
Innbundet / 2020 / Engelsk

Produktdetaljer

ISBN
9783030372026
Publisert
2020-04-04
Utgiver
Vendor
Springer Nature Switzerland AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Forfatter
Di Pietro Daniele Antonio
Droniou, Jérôme

Biographical note

Daniele A. Di Pietro has been a Full Professor since 2012 and Deputy Director of Institut Montpelliérain Alexander Grothendieck at the University of Montpellier (France) since 2019. He is the author of two research monographs published by Springer and more than 80 scientific papers in refereed international journals or conference proceedings. His research fields include the development and analysis of advanced numerical methods for partial differential equations, with applications to fluid and solid mechanics and porous media. Over the course of his career, he has supervised ten PhD students and six postdoctoral fellows.  

 

Jérôme Droniou was a Full Professor in France before moving to Monash university (Australia), where he has been an Associate Professor in the School of Mathematics  since 2018, and head of the applied and computational section  since 2019. He has authored two research monographs and more than 80 peer-reviewed articles and conference proceedings on theoretical and numerical analysis of partial differential equations. His current research interests revolve around the development of numerical methods for complex applications, and the design of mathematical tools to analyse the convergence of these methods. He has supervised a dozen PhD students and postdoctoral fellows in France and Australia.

Hybrid High-Order Method for Polytopal Meshes Design, Analysis, and Applications

Di Pietro Daniele Antonio Droniou, Jérôme
Innbundet / 2020 / Engelsk
Di Pietro Daniele Antonio Droniou, Jérôme
Innbundet / 2020 / Engelsk
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This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.  
Les mer
This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics.
Les mer
Part I: Foundations.- 1 Setting.- 2 Basic principles of Hybrid High-Order methods: The Poisson problem.- 3 Variable di_usion and di_usion–advection–reaction.- 4 Complements on pure di_usion.- 5 Variations and comparison with other methods.- Part II: Applications to advanced models.- 6 p-Laplacian and Leray–Lions.- 7 Linear elasticity.- 8 Stokes.- 9 Navier–Stokes.- Part III: Appendix.- 10 Appendix A: Error analysis setting for schemes in fully discrete formulation.- 11 Appendix B: Implementation.  
Les mer
This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.
Les mer
  
Provides an introduction to the design and the mathematical aspects of Hybrid High-Order methods for diffusive problems Addresses a panel of applications to advanced models in computational mechanics Provides powerful tools for the analysis of discretisation methods for partial differential equations Designed for graduate students and researchers in applied mathematics and numerical analysis
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

Relaterte produkter

  

This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.  
Les mer
This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics.
Les mer
Part I: Foundations.- 1 Setting.- 2 Basic principles of Hybrid High-Order methods: The Poisson problem.- 3 Variable di_usion and di_usion–advection–reaction.- 4 Complements on pure di_usion.- 5 Variations and comparison with other methods.- Part II: Applications to advanced models.- 6 p-Laplacian and Leray–Lions.- 7 Linear elasticity.- 8 Stokes.- 9 Navier–Stokes.- Part III: Appendix.- 10 Appendix A: Error analysis setting for schemes in fully discrete formulation.- 11 Appendix B: Implementation.  
Les mer
This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.
Les mer
  
Provides an introduction to the design and the mathematical aspects of Hybrid High-Order methods for diffusive problems Addresses a panel of applications to advanced models in computational mechanics Provides powerful tools for the analysis of discretisation methods for partial differential equations Designed for graduate students and researchers in applied mathematics and numerical analysis
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

Produktdetaljer

ISBN
9783030372026
Publisert
2020-04-04
Utgiver
Vendor
Springer Nature Switzerland AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Forfatter
Di Pietro Daniele Antonio
Droniou, Jérôme

Biographical note

Daniele A. Di Pietro has been a Full Professor since 2012 and Deputy Director of Institut Montpelliérain Alexander Grothendieck at the University of Montpellier (France) since 2019. He is the author of two research monographs published by Springer and more than 80 scientific papers in refereed international journals or conference proceedings. His research fields include the development and analysis of advanced numerical methods for partial differential equations, with applications to fluid and solid mechanics and porous media. Over the course of his career, he has supervised ten PhD students and six postdoctoral fellows.  

 

Jérôme Droniou was a Full Professor in France before moving to Monash university (Australia), where he has been an Associate Professor in the School of Mathematics  since 2018, and head of the applied and computational section  since 2019. He has authored two research monographs and more than 80 peer-reviewed articles and conference proceedings on theoretical and numerical analysis of partial differential equations. His current research interests revolve around the development of numerical methods for complex applications, and the design of mathematical tools to analyse the convergence of these methods. He has supervised a dozen PhD students and postdoctoral fellows in France and Australia.

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