We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equation for the Euler equation. Based on the multiscale analysis in the Lagrangian formulation, we also derive the corresponding multiscale analysis in the Eulerian formulation. Moreover, our multiscale analysis reveals some interesting structure for the Reynolds stress term, which provides a theoretical base for establishing systematic multiscale modeling of 2-D incompressibleow.

A parallel domain decomposition algorithm of Schwarz type is introduced to solve the mixed finite element equation for the Dirichlet boundary value problem of a secondorder partial differential equation of elliptic type and convergence of this algorithm is analyzed.

In this paper, we give two finite difference streamline diffusion (FDSD) schemes for solving linear Sobolev equations with convection-dominated term. Stability and optimal error estimates for them are derived in suitable norms.

A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes equations were considered. For the stationary equation, optimal H1 andL2-error estimates are derived under the standard regularity assumption on the finite element partition (the LBB-condition is not required). For the evolutionary equation, optimal L2 estimates are derived under the conventional Raviart-Thomas spaces.

提出具有对称正定特性的混合元格式求解非稳态半导体器件瞬态模拟问题提出一个最小二乘混合元方法、一个新的具有分裂和对称正定性质的混合元格式和一个解经典混合元方程的对称正定迭代格式求解电场位势和电场强度方程提出一个最小二乘混合元格式求解关于电子与空穴浓度的非稳态对流扩散方程，浓度函数和流函数被同时求解采用标准的有限元方法求解热传导方程建立了误差分析理论。