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 …
fully nonlinear partial differential equations (PDEs), a relatively new subarea within …
Adaptivity with moving grids
In this article we survey r-adaptive (or moving grid) methods for solving time-dependent
partial differential equations (PDEs). Although these methods have received much less …
partial differential equations (PDEs). Although these methods have received much less …
Convergent finite difference solvers for viscosity solutions of the elliptic Monge–Ampère equation in dimensions two and higher
BD Froese, AM Oberman - SIAM Journal on Numerical Analysis, 2011 - SIAM
The elliptic Monge–Ampère equation is a fully nonlinear partial differential equation that
originated in geometric surface theory and has been applied in dynamic meteorology …
originated in geometric surface theory and has been applied in dynamic meteorology …
Two numerical methods for the elliptic Monge-Ampere equation
JD Benamou, BD Froese… - … Modelling and Numerical …, 2010 - cambridge.org
The numerical solution of the elliptic Monge-Ampère Partial Differential Equation has been a
subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial …
subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial …
Convergent filtered schemes for the Monge--Ampère partial differential equation
BD Froese, AM Oberman - SIAM Journal on Numerical Analysis, 2013 - SIAM
The theory of viscosity solutions has been effective for representing and approximating weak
solutions to fully nonlinear partial differential equations such as the elliptic Monge--Ampère …
solutions to fully nonlinear partial differential equations such as the elliptic Monge--Ampère …
A numerical method for the elliptic Monge--Ampère equation with transport boundary conditions
BD Froese - SIAM Journal on Scientific Computing, 2012 - SIAM
The problem of optimal mass transport arises in numerous applications, including image
registration, mesh generation, reflector design, and astrophysics. One approach to solving …
registration, mesh generation, reflector design, and astrophysics. One approach to solving …
𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
In this paper, we develop and analyze $\mathcal {C}^ 0$ penalty methods for the fully
nonlinear Monge-Ampère equation $\det (D^ 2 u)= f $ in two dimensions. The key idea in …
nonlinear Monge-Ampère equation $\det (D^ 2 u)= f $ in two dimensions. The key idea in …
Mixed finite element methods for the fully nonlinear Monge–Ampère equation based on the vanishing moment method
This paper studies mixed finite element approximations of the viscosity solution to the
Dirichlet problem for the fully nonlinear Monge–Ampère equation \det(D^2u^0)=f\,(>0) based …
Dirichlet problem for the fully nonlinear Monge–Ampère equation \det(D^2u^0)=f\,(>0) based …
Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-
order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 …
order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 …
[图书][B] Variational methods for the numerical solution of nonlinear elliptic problems
R Glowinski - 2015 - SIAM
During a very large part of his career the author of this book has been interested in the
application of variational methods to problems from science and engineering, particularly …
application of variational methods to problems from science and engineering, particularly …