Dongwoo Sheen

P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems

A P1 -nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements, which contain quadratic polynomials or polynomials of degree greater than 2, our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges. One of the benefits of using our element is convenience in using rectangular or quadrilateral meshes with the least degrees of freedom among the nonconforming quadrilateral elements. An optimal rate of convergence is obtained. Also a nonparametric reference scheme is introduced in order to systematically compute stiffness and mass matrices on each quadrilateral. An extension of the P1 -nonconforming element to three dimensions is also given. Finally, several numerical results are reported to confirm the effective nature of the proposed new element.

The inverse conductivity problem with one measurement: stability and estimation of size

We consider the inverse problem to the refraction problem div

FREQUENCY DOMAIN TREATMENT OF ONE-DIMENSIONAL SCALAR WAVES

((1 + (k -1)\chi_D)\nabla u)=0 in

APPROXIMATION OF SCALAR WAVES IN THE SPACE-FREQUENCY DOMAIN

\Omega

A locking-free nonconforming finite element method for planar linear elasticity

and

Turing instability for a ratio-dependent predator–prey model with diffusion

\pd{u}{\nu}=g

Numerical identification of discontinuous conductivity coefficients

on

A NONCONFORMING MIXED FINITE ELEMENT METHOD FOR MAXWELL'S EQUATIONS

\partial\Omega

A locking-free immersed finite element method for planar elasticity interface problems

. The inverse problem is to determine the size and the location of an unknown object D from the boundary measurement

Nonconforming finite element methods for the simulation of waves in viscoelastic solids

\Lambda_D(g)=u|_{\bO}