Uniform in discretization error estimates for convection dominated convection-diffusion problems
Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems.
Uniformly convergent adaptive methods for a class of parametric operator equations∗
We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
Uniformly convergent adaptive methods for a class of parametric operator equations∗
We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
Uniformly Convergent Difference Schemes for Singularly Perturbed Parabolic Diffusion-Convection Problems Without Turning Points.
Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes
We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.
Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms
Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the...
Universal approximation by systems of hill functions
Upstream weighting and mixed finite elements in the simulation of miscible displacements
Upwind computation of steady planar flames with complex chemistry
Upwind FEM for convection dominated elliptic problems
Usage of modular scissors in the implementation of FEM
Finite Element Method (FEM) is often perceived as a unique and compact programming subject. Despite the fact that many FEM implementations mention the Object Oriented Approach (OOA), this approach is used completely, only in minority of cases in most real-life situations. For example, one of building stones of OOA, the interface-based polymorphism, is used only rarely. This article is focusing on the design reuse and at the same time it gives a complex view on FEM. The article defines basic principles...
Use of the multigrid methods for heat radiation problem.
Using successive approximations for improving the convergence of GMRES method
In this paper, our attention is concentrated on the GMRES method for the solution of the system of linear algebraic equations with a nonsymmetric matrix. We perform pre-iterations before starting GMRES and put for the initial approximation in GMRES. We derive an upper estimate for the norm of the error vector in dependence on the th powers of eigenvalues of the matrix . Further we study under what eigenvalues lay-out this upper estimate is the best one. The estimate shows and numerical...
Validation of numerical simulations of a simple immersed boundary solver for fluid flow in branching channels
This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the channel geometry. The numerical results obtained by this new solver are compared with the numerical simulations of the older finite volume method code and with the results obtained with OpenFOAM. The aim of this work is to verify whether the immersed boundary method is suitable for fluid flow in channels...
Variational approximation methods for eigenvalues. Convergence theorems
Variational approximation of flux in conforming finite element methods for elliptic partial differential equations : a model problem
We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence.
Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations
Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.
Variational formulation and analysis of a linearized 2-D model with no axial symmetry for a two-phase water-petroleum flow.
Variational Principles and Convergence of Finite Element Approximations of a Holonomic Elastic-Plastic Problem.