The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
The finite element solution of parabolic equations
In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in -dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in -norm of the method.
The finite element solution of second order elliptic problems with the Newton boundary condition
The convergence of the finite element solution for the second order elliptic problem in the -dimensional bounded domain with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the and norms are obtained.
The version of the boundary element method on polygonal domains with quasiuniform meshes
The version of the finite element method with quasiuniform meshes
The hp-version of the boundary element method with quasi-uniform meshes in three dimensions
We prove an a priori error estimate for the hp-version of the boundary element method with hypersingular operators on piecewise plane open or closed surfaces. The underlying meshes are supposed to be quasi-uniform. The solutions of problems on polyhedral or piecewise plane open surfaces exhibit typical singularities which limit the convergence rate of the boundary element method. On closed surfaces, and for sufficiently smooth given data, the solution is H1-regular whereas, on open surfaces, edge...
The mixed problem for the Laplace equation on the rectangle
The Mortar method in the wavelet context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
The Mortar Method in the Wavelet Context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
The -version of the finite element method for elliptic equations of order
The role of the patch test in 2D atomistic-to-continuum coupling methods∗
For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...
The role of the patch test in 2D atomistic-to-continuum coupling methods∗
For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...
The second order projection method in time for the time-dependent natural convection problem
We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is...
Total Flux Estimates for a Finite Element Approximation of the Dirichlet Problem Using the Boundary Penalty Method.
Triangular mesh analysis with application on hip bone
Shape analyses and similarity measuring is a very often solved problem in computer graphics. The shape distribution approach based on shape functions is frequently used for this determination. The experience from a comparison of ball-bar standard triangular meshes was used to match hip bones triangular meshes. The aim is to find relation between similarity measures obtained by shape distributions approach.
Two Families of Mixed Finite Elements for Second Order Elliptic Problems.
Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra.
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H. In the second step, the problem is linearized by substituting into the non-linear term, the velocity uH computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h. This approach is motivated by the fact that,...
Two-level stabilized nonconforming finite element method for the Stokes equations
In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size and a large stabilized Stokes...