This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusionβ(u)+A(u)+g(x,u,Du)■f,where A is a Leray-Lions operator fr...This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusionβ(u)+A(u)+g(x,u,Du)■f,where A is a Leray-Lions operator from W^(1,p)_(0)(Ω)into its dual,βmaximal monotone mapping such that 0∈β(0),while g(x,s,ξ)is a nonlinear term which has a growth condition with respect toξand no growth with respect to s but it satisfies a signcondition on s.The right hand side f is assumed to belong to L^(1)(Ω).展开更多
We investigate the practical implementation of a high-order explicit time-stepping method based on polynomial approximations,for possible application to large-scale problems in electromagnetics.After the spatial discr...We investigate the practical implementation of a high-order explicit time-stepping method based on polynomial approximations,for possible application to large-scale problems in electromagnetics.After the spatial discretization by a high-order discontinuous Galerkin method,we obtain a linear system of differential equations of the form,∂tY(t)=HY(t)+S(t),where H is a matrix containing the spatial derivatives and t is the time variable.The formal solution can be written in terms of the matrix exponential,exp(tH),acting on some vectors.We introduce a general family of time-integrators based on the approximation of exp(tH)by Jacobi polynomial expansions.We discuss the efficient implementation of this technique,and based on some test problems,we compare the virtues and shortcomings of the algorithm.We also demonstrate how these schemes provide an efficient alternative to standard explicit integrators for computing solutions over long time intervals.展开更多
文摘This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusionβ(u)+A(u)+g(x,u,Du)■f,where A is a Leray-Lions operator from W^(1,p)_(0)(Ω)into its dual,βmaximal monotone mapping such that 0∈β(0),while g(x,s,ξ)is a nonlinear term which has a growth condition with respect toξand no growth with respect to s but it satisfies a signcondition on s.The right hand side f is assumed to belong to L^(1)(Ω).
基金supported by the DGA(Direction Generale de l’Armement)under contract No.2009.34.0010.
文摘We investigate the practical implementation of a high-order explicit time-stepping method based on polynomial approximations,for possible application to large-scale problems in electromagnetics.After the spatial discretization by a high-order discontinuous Galerkin method,we obtain a linear system of differential equations of the form,∂tY(t)=HY(t)+S(t),where H is a matrix containing the spatial derivatives and t is the time variable.The formal solution can be written in terms of the matrix exponential,exp(tH),acting on some vectors.We introduce a general family of time-integrators based on the approximation of exp(tH)by Jacobi polynomial expansions.We discuss the efficient implementation of this technique,and based on some test problems,we compare the virtues and shortcomings of the algorithm.We also demonstrate how these schemes provide an efficient alternative to standard explicit integrators for computing solutions over long time intervals.
