In this paper, we present a weak Galerkin （WG） mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled metho...In this paper, we present a weak Galerkin （WG） mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the L^2 for the flux and H1 for the scalar function. Also an optimal order error estimate in L^2 is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.展开更多
In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we pr...In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).展开更多
文摘In this paper, we present a weak Galerkin （WG） mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the L^2 for the flux and H1 for the scalar function. Also an optimal order error estimate in L^2 is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.
基金supported by National Natural Science Foundation of China (Grant Nos.60971121,10590353,90916027,10725210)Major State Basic Research Development Program of China (973Program) (Grant No.2010CB832702)+1 种基金the State Key Laboratory of Science and Engineering Computing,Natural Science Foundation of Zhejiang Province,China (Grant No.Y6090108)Postdoctoral Science Foundation of China (Grant No.20090451454)
文摘In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).
