Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems

This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in IFE functions. With the enhanced stability due to the added penalty, not only these IFE methods can be proven to have the optimal convergence rate in the H1-norm provided that the exact solution has sufficient regularity, but also numerical results indicate that their convergence rates in both the H1-norm and the L2-norm do not deteriorate when the mesh becomes finer which is a shortcoming of the classic IFE methods in some situations. Trace inequalities are established for both linear and bilinear IFE functions that are not only critical for the error analysis of these new IFE methods, but also are of a great potential to be useful in error analysis for other IFE methods

Graduate Recital: Yanping Lin

Kemp Recital HallMarch 25, 2012Sunday Evening7: 00 p.m

Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions

AbstractWe derive optimal L2 error estimates for semi-discrete finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions. A new projection is introduced and used in the error analysis

Control of Soybean Aphids with Super Low-Dose Spraying: Efficacy and Labor Savings

The soybean aphid (Aphis glycines Mats.) is a major insect pest in soybean production areas, with annual occurrences causing serious damage to the soybean crops. The purpose of this experiment was to compare the control effect on soybean aphid and working efficacy of two methods of spraying with Dimethoate, namely, super-low volume spraying and conventional volume spraying, carried on the back with a manual compression operation. The results obtained are as follows.Originating text in Chinese.Citation: Li, Yong, Lin, Peili, Liu, Yanping. (1989). Control of Soybean Aphids with Super Low-Dose Spraying: Efficacy and Labor Savings. Agricultural Sciences [in Heilongjiang Province], 1, 34-35