In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic mu...In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the non-symmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.展开更多
lit the present paper, quasilinear elliptic hemivariational inequalities as a generalization to nonconvex functionals of the elliptic variational inequalities are studied. This extension is strongly motivated by vario...lit the present paper, quasilinear elliptic hemivariational inequalities as a generalization to nonconvex functionals of the elliptic variational inequalities are studied. This extension is strongly motivated by various problems in mechanics. By using the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, the existence of solutions is proved.展开更多
For γ≥1 we consider the solution u=u（x） of the Dirichlet boundary value problem Δu ＋ u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate u（x）=p（δ（x））[1＋A（x）（log 1/δ（x）^-6],where p（r） ≈ r ...For γ≥1 we consider the solution u=u（x） of the Dirichlet boundary value problem Δu ＋ u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate u（x）=p（δ（x））[1＋A（x）（log 1/δ（x）^-6],where p（r） ≈ r r√2 log（1/r） near r = 0,δ（x） denotes the distance from x to δΩ, 0 〈ε 〈 1/2, and A（x） is a bounded function. For 1 〈 γ 〈 3 we findu（x）=（γ＋1/√2（γ-1）δ（x））^2/γ＋[1＋A（x）（δ（x））2γ-1/γ＋1]For γ3= we prove thatu（x）=（2δ（x））^1/2[1＋A（x）δ（x）log 1/δ（x）]展开更多
In this paper, we shall deal with quasilinear elliptic hemivariational inequalities. By the use of the theory of multivalued pseudomonotone mappings, we will prove the existence of solutions.
We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a...We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a Hilbert space via the local linking theorem. Different from the works in the literature, the new theorem is constructed under the(C)* condition instead of (PS)* condition.展开更多
An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization ...An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.展开更多
文摘In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the non-symmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.
文摘lit the present paper, quasilinear elliptic hemivariational inequalities as a generalization to nonconvex functionals of the elliptic variational inequalities are studied. This extension is strongly motivated by various problems in mechanics. By using the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, the existence of solutions is proved.
文摘For γ≥1 we consider the solution u=u（x） of the Dirichlet boundary value problem Δu ＋ u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate u（x）=p（δ（x））[1＋A（x）（log 1/δ（x）^-6],where p（r） ≈ r r√2 log（1/r） near r = 0,δ（x） denotes the distance from x to δΩ, 0 〈ε 〈 1/2, and A（x） is a bounded function. For 1 〈 γ 〈 3 we findu（x）=（γ＋1/√2（γ-1）δ（x））^2/γ＋[1＋A（x）（δ（x））2γ-1/γ＋1]For γ3= we prove thatu（x）=（2δ（x））^1/2[1＋A（x）δ（x）log 1/δ（x）]
基金the funds of State Educational Commission of China for Returned Scholars from Abroad.
文摘In this paper, we shall deal with quasilinear elliptic hemivariational inequalities. By the use of the theory of multivalued pseudomonotone mappings, we will prove the existence of solutions.
文摘We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a Hilbert space via the local linking theorem. Different from the works in the literature, the new theorem is constructed under the(C)* condition instead of (PS)* condition.
文摘An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.
