A mixed finite element method for fourth order elliptic equations with variable coefficients

Closed form numerical solutions of variable coefficient linear second-order elliptic problems

“…This fact checks the consistency of explicit difference scheme (10). Note that due to the truncation error is of order O(h + k 2 ) we have refined in axis x.…”

“…obtaining the explicit difference scheme (10) where the parameter α was defined in (7). Now we are going to study the consistency of constructed scheme (10) with Eq.…”

“…Apart from some techniques such as meshless methods [1,2] and those based on particular transformations used to solve special problems [3,4], the most used are related mesh methods as the finite difference method [5,6,7], the finite-volume method [8,9] and the finite element method [10,11].…”

An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model

“…As a resuit, it would be interesting to study the nature and behaviour of finite element approximations of degree one for oe in the global discretization scheme developed hère. Other different choices such as the use of quadratic éléments for co in (6.4) and éléments of degree one for y/ in équation (6.3) may further improve the results of approximation, but this is nothing but a conjecture (see [3]). …”

Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients

“…Indeed to our knowledge, [8] is probably the first publication on the estimates for the combined effect of boundary approximation and numerical integration on the mixed finite element approximation of (simple) eigenvalues and eigenvectors of 4th order self-adjoint eigenvalue problems with variable/constant coefficients, many proofs in which, as stated earlier, have remained quite technical in spite of the best efforts of the authors to avoid these technical aspects in some proofs. The present paper, the results of which were announced in [8] (see also [31]), relies heavily on [10] for the corresponding source problem ( [9] contains error estimates due to polygonal approximation of the curved boundary along with numerical integration for the same source problem) and also on the results of [4] on the mixed method scheme (see also [33,36]) for polygonal domains. For other interesting references on eigenvalue approximations, we refer to [2,15].…”