Approximation of a fourth order variational inequality
Approximation of a Martensitic Laminate with Varying Volume Fractions
We give results for the approximation of a laminate with varying volume fractions for multi-well energy minimization problems modeling martensitic crystals that can undergo either an orthorhombic to monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfy the corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energy for the approximation of the limiting macroscopic deformation and...
Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method
By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally,...
Approximation of an elliptic boundary value problem with unilateral constraints
Approximation of General Arch Problems by Straight Beam Elements
Approximation of Hopf Bifurcation.
Approximation of solution branches for semilinear bifurcation problems
Approximation of solution branches for semilinear bifurcation problems
This note deals with the approximation, by a P1 finite element method with numerical integration, of solution curves of a semilinear problem. Because of both mixed boundary conditions and geometrical properties of the domain, some of the solutions do not belong to H2. So, classical results for convergence lead to poor estimates. We show how to improve such estimates with the use of weighted Sobolev spaces together with a mesh “a priori adapted” to the singularity. For the H1 or L2-norms, we...
Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements
We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling is...
Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements
We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling...
Approximation of Time-Dependent Free Boundaries
Approximation of Tricomi Problem with Neumann Boundary Condition.
Aproximación de un problema elíptico singular mediante elementos finitos isoparamétricos degenerados.
Arch beam models: finite element analysis and superconvergence.
Asymptotic Error Expansion and Richardson Extrapolation for Linear Finite Elements.
Asymptotic Expansions and L...-Error Estimates for Mixed Finite Element Methods for Second Order Elliptic Problems.
Asymptotic lower bounds for eigenvalues by nonconforming finite element methods.
Asymptotic lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients
In this paper, using a new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain asymptotic lower bounds of eigenvalues for the Steklov eigenvalue problem with variable coefficients on -dimensional domains (). In addition, we prove that the corrected eigenvalues converge to the exact ones from below. The new result removes the conditions of eigenfunction being singular and eigenvalue being large enough, which are usually required in the existing arguments about...
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x 1, x 2) at the vertices of a regular triangulation T h composed both of rectangles and triangles is presented. The method assumes that only the interpolant Πh[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T h is known. A complete analysis of this method is an extension of the complete analysis concerning the finite...
Basic compactness properties of nonconforming and hybrid finite element spaces