In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an
attractive approach for numerical simulations of compressible flows. This paper presents an …

This article surveys the recent developments in computational methods for second order
fully nonlinear partial differential equations (PDEs), a relatively new subarea within …

This book is about adaptive mesh generation and moving mesh methods for the numerical
solution of time-dependent partial differential equations. It presents a general framework and …

A numerical method for the solution of the elliptic Monge–Ampère Partial Differential
Equation, with boundary conditions corresponding to the Optimal Transportation (OT) …

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 …

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 …

The problem of optimal mass transport arises in numerous applications, including image
registration, mesh generation, reflector design, and astrophysics. One approach to solving …

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 …

2. Hyper-reduction methods 2.1 Parametrized integrals 2.2 Empirical quadrature methods
2.3 Empirical interpolation methods 2.4 Integral interpolation methods 3. First-order …

Nuclear morphology and structure as visualized from histopathology microscopy images can
yield important diagnostic clues in some benign and malignant tissue lesions. Precise …