On a linearized p-Laplace equation with rapidly oscillating coefficients

Sensitivity analysis of aquifer parameter estimations based on the Laplace equation with linearized boundary conditions

[1] Estimates of aquifer parameters, saturated hydraulic conductivity, and drainable porosity were obtained by an analytical solution of the two-dimensional Laplace equation with linearized boundary conditions and were compared to prescribed parameters in a finite element model that simulated drainage of a coupled system of unsaturated/saturated flow. Boundary conditions prerequisite for the an...

Homogenization of linear hyperbolic stochastic partial differential equation with rapidly oscillating coefficients: The two scale convergence method

In this paper we establish new homogenization results for stochastic linear hyperbolic equations with periodically oscillating coefficients. We first use the multiple expansion method to drive the homogenized problem. Next we use the two scale convergence method and Prokhorov’s and Skorokhod’s probabilistic compactness results. We prove that the sequence of solutions of the original problem con...

Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients

A new multiscale finite element method is presented for solving the elliptic equations with rapidly oscillating coefficients. The proposed method is based on asymptotic analysis and careful numerical treatments for the boundary corrector terms by virtue of the recovery technique. Under the assumption that the oscillating coefficient is periodic, some superconvergence results are derived, which ...

Multiscale Computation of a Steklov Eigenvalue Problem with Rapidly Oscillating Coefficients

In this paper we consider the multiscale computation of a Steklov eigenvalue problem with rapidly oscillating coefficients. The new contribution obtained in this paper is a superapproximation estimate for solving the homogenized Steklov eigenvalue problem and to present a multiscale numerical method. Numerical simulations are then carried out to validate the theoretical results reported in the ...

A Three-Scale Finite Element Method for Elliptic Equations with Rapidly Oscillating Periodic Coefficients