This paper studies mixed finite element approximations of the viscosity solution to the Dirichlet problem for the fully nonlinear Mongeâ€“AmpÃ¨re equation det(D2u0) = f (> 0) based on the vanishingâ€¦ (More)

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, isâ€¦ (More)

This paper develops and analyzes some interior penalty discontinuous Galerkin methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary conditionâ€¦ (More)

In this paper we present PDE and finite element analyses for a system of PDEs consisting of the Darcy equation and the Cahnâ€“Hilliard equation, which arises as a diffuse interface model for theâ€¦ (More)

We propose and analyze a semi-discrete and a fully discrete mixed finite element method for the Cahn-Hilliard equation ut + (Îµ uâˆ’ Îµâˆ’1f (u)) = 0, where Îµ > 0 is a small parameter. Error estimatesâ€¦ (More)

We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow,â€¦ (More)

This paper develops and analyzes finite element Galerkin and spectral Galerkin methods for approximating viscosity solutions of the fully nonlinear Monge-AmpÃ¨re equation det(D2u0) = f (> 0) based onâ€¦ (More)

In this paper we develop and analyze some interior penalty hpdiscontinuous Galerkin (hp-DG) methods for the Helmholtz equation with first order absorbing boundary condition in two and threeâ€¦ (More)