We consider bilinear forms A(-, •) connected with second-order elliptic problems and assume that for uh in a finite element space S¡,, we have A(u U),, x) = F(x) for x m Sh with local compact support. We give local estimates for u Uf, in L^ and W^ of the type "local best approximation plus weak outside influences plus the local size of F ".

in this paper, an advanced formulation of the spectral finite element method (sfem) is presented and applied in order to carry out site response analysis of 2d topographic structures subjected to vertically propagating incident in-plane waves in time-domain. the accuracy, efficiency and applicability of the formulation are demonstrated by solving some wave scattering examples. a numerical param...

modelling of crack propagation by finite element method under mixed mode conditions is of prime importance in fracture mechanics. this paper describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. crack growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion,...

We focus here on a class of fourth-order parabolic equations that can be written as system second-order by introducing an auxiliary variable. design novel fully discrete mixed finite element method to approximate these equations. In our approach, we propose new techniques using the backward differentiation formula for time derivative and special technique approximation nonlinear terms. The use ...

A (v, K, A) packing design of order v, block size K, and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most L blocks. The packing problem is to determine the maximum number of blocks in a packing design. Packing with 1= 2 is called bipacking. In this paper we solve the bipacking problem in the case K = 5 and v = 13 (mod 20).