Error Estimates of a Galerkin Method for Some Nonlinear Sobolev Equations in one Space Dimension.
Error estimates of a linear approximation scheme for nonlinear diffusion problems.
Error estimates of a numerical method for a class of nonlinear evolution equations
Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part . The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for the linearization...
Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part Γn. The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for...
Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem
This paper deals with an initial and boundary value problem describing the quasistatic evolution of rate-type viscoplastic materials. Using a fixed point property, an iterative method in the study of this problem is proposed. A concrete algorithm as well as some numerical results in the one-dimensional case are also presented.
Error estimation and adaptivity for nonlinear FE analysis
An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem:...
Error estimation and optimization of the functional algorithms of a random walk on a grid which are applied to solving the Dirichlet problem for the Helmholtz equation.
Error estimation for finite element solutions on meshes that contain thin elements
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if ``bad'' elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.
Error estimation of pseudospectral method for solving the barotropic vorticity equation.
Error estimation on the Padé approximation of transfer functions via the Lanczos process.
Error evaluation of approximate solutions for sum-difference equations in two variables.
Error inequalities for a generalized quadrature rule.
Error inequalities for a quadrature formula of open type.
Error minimization in approximate solution of integral equations
Error of the two-step BDF for the incompressible Navier-Stokes problem
The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional case....
Error of the two-step BDF for the incompressible Navier-Stokes problem
The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional...
Error-Bounds for Finite Element Method.
Error-estimates for the method of least squares of finding eigenvalues and eigenfunctions
Error-estimates for the Ritz's method of finding eigenvalues and eigenfunctions