This paper is to develop immersed finite element (IFE) functions for solving second order
elliptic boundary value problems with discontinuous coefficients and non-homogeneous …

We show that the fourth order accurate finite difference implementation of continuous finite
element method with tensor product of quadratic polynomial basis is monotone thus satisfies …

Discrete maximum principles (DMPs) are established for finite element approximations of
systems of nonlinear parabolic partial differential equations with mixed boundary and …

We propose three new finite element methods for solving boundary value problems of 4th
order differential equations with discontinuous coefficients. Typical differential equations …

FEM for a linear and nonlinear elliptic interface problems with discontinuous coefficients is
presented. The standard basis functions are modified near the interface in such a way that …

In this article, we consider two‐grid finite element methods for solving semilinear interface
problems in d space dimensions, for d= 2 or d= 3. We consider semilinear problems with …

On rectangular meshes, the simplest spectral element method for elliptic equations is the
classical Lagrangian Q k finite element method with only (k+ 1)-point Gauss-Lobatto quadra …

The paper is devoted to the problem of verification of accuracy of approximate solutions
obtained in computer simulations. This problem is strongly related to a posteriori error …

The discrete maximum principle (DMP) is an important measure of the qualitative reliability
of the applied numerical scheme for elliptic problems. This paper starts with formulating …

We propose the damped inexact Newton method, coupled with preconditioned inner
iterations, to solve the finite element discretization of a class of nonlinear elliptic interface …