Finite difference methods for time dependent, linear differential algebraic equations

AbstractRecently the authors developed a global reduction procedure for linear, time-dependent DAE that transforms their solutions of smaller systems of ODE's. Here it is shown that this reduction allows for the construction of simple, convergent finite difference schemes for such equations

Intrinsic Isotropy Subgroups of Finite Groups

AbstractThis paper discusses general properties of intrinsic isotropy subgroups of finite groups, a notion recently introduced by the author, and motivated by the relevance of such subgroups in problems of bifurcation with symmetry. The main results established here are that groups are or are not intrinsic isotropy subgroups of themselves depending only upon their order being odd or even, and the characterization of 2-nilpotent groups as an optimal class of groups having a unique maximal intrinsic isotropy subgroup. The simplest case when uniqueness is lost is shown to correspond to groups whose structure generalizes that of A

On boundary-hybrid finite element methods for the Laplace equation

About two decades ago, I. Babu ka, J.T. Oden and J.K. Lee introduced finite element methods that calculate the normal derivative of the solution along the mesh interfaces and recover the solution via local Neumann problems. These methods for the treatment of the homogeneous Laplace equation were called ‘boundary-hybrid methods’. The approach was revisited in [12] for general symmetric and positive definite elliptic equations with homogeneous boundary conditions. The new approximation is nonconforming and lends itself well for an a posteriori error estimator for conforming finite element approximations. Numerical tests presented in [12] corroborated that the error estimates are accurate and cheap for conforming approximations. This paper provides the iterative solution methods and Galerkin discretization methods on which the numerical approximations in [12] were based