Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations
This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDEs), a relatively new subarea within numerical PDEs. Due to their ever increasing importance in mathematics itself (e.g., differential geometry and PDEs) and in ma...
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| Published in | SIAM review Vol. 55; no. 2; pp. 205 - 267 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2013
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| Online Access | Get full text |
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| Abstract | This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDEs), a relatively new subarea within numerical PDEs. Due to their ever increasing importance in mathematics itself (e.g., differential geometry and PDEs) and in many scientific and engineering fields (e.g., astrophysics, geostrophic fluid dynamics, grid generation, image processing, optimal transport, meteorology, mathematical finance, and optimal control), numerical solutions to fully nonlinear second order PDEs have garnered a great deal of interest from the numerical PDE and scientific communities. Significant progress has been made for this class of problems in the past few years, but many problems still remain open. This article intends to introduce these current advancements and new results to the SIAM community and generate more interest in numerical methods for fully nonlinear PDEs. |
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| AbstractList | This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDE), a relatively new subarea within numerical PDEs. Due to their ever increasing importance in mathematics itself (e.g., differential geometry and PDEs) and in many scientific and engineering fields (e.g., astrophysics, geostrophic fluid dynamics, grid generation, image processing, optimal transport, meteorology, mathematical finance, and optimal control), numerical solutions to fully nonlinear second order PDEs have garnered a great deal of interest from the numerical PDE and scientific communities. Significant progress has been made for this class of problems in the past few years, but many problems still remain open. This article intends to introduce these current advancements and new results to the SIAM community and generate more interest in numerical methods for fully nonlinear PDEs. [PUBLICATION ABSTRACT] This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDEs), a relatively new subarea within numerical PDEs. Due to their ever increasing importance in mathematics itself (e.g., differential geometry and PDEs) and in many scientific and engineering fields (e.g., astrophysics, geostrophic fluid dynamics, grid generation, image processing, optimal transport, meteorology, mathematical finance, and optimal control), numerical solutions to fully nonlinear second order PDEs have garnered a great deal of interest from the numerical PDE and scientific communities. Significant progress has been made for this class of problems in the past few years, but many problems still remain open. This article intends to introduce these current advancements and new results to the SIAM community and generate more interest in numerical methods for fully nonlinear PDEs. |
| Author | Feng, Xiaobing Neilan, Michael Glowinski, Roland |
| Author_xml | – sequence: 1 givenname: Xiaobing surname: Feng fullname: Feng, Xiaobing – sequence: 2 givenname: Roland surname: Glowinski fullname: Glowinski, Roland – sequence: 3 givenname: Michael surname: Neilan fullname: Neilan, Michael |
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| Snippet | This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDEs), a relatively new... This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDE), a relatively new... |
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| SubjectTerms | Applied mathematics Astrophysics Communities Computer science Engineering Estimates Geometry Image processing Lagrange multiplier Mathematical models Meteorology Nonlinear differential equations Nonlinear programming Nonlinearity Numerical analysis Partial differential equations Studies SURVEY and REVIEW |
| Title | Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations |
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