Error Estimates for Semidiscrete Galerkin Type Approximations for Semilinear Evolution Equations with Nonsmooth Initial Data.
Error estimates for some mixed finite element methods for parabolic type problems
Error estimates for Stokes problem with Tresca friction conditions
In this paper, we present and study a mixed variational method in order to approximate, with the finite element method, a Stokes problem with Tresca friction boundary conditions. These non-linear boundary conditions arise in the modeling of mold filling process by polymer melt, which can slip on a solid wall. The mixed formulation is based on a dualization of the non-differentiable term which define the slip conditions. Existence and uniqueness of both continuous and discrete solutions of these...
Error estimates for the assumed stresses hybrid methods in the approximation of 4th order elliptic equations
Error estimates for the Coupled Cluster method
The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...
Error estimates for the finite element solutions of variational inequalities.
Error estimates for the finite element solutions of variational inequalities
Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations.
Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation provides a variational framework suitable for discretization using plane wave solutions of an appropriate adjoint equation. Currently convergence of the method is only proved on the boundary of the domain. However substantial computational evidence exists showing that the method also converges throughout the domain of the Helmholtz equation. In this paper we exploit the fact that the UWVF is essentially an upwind discontinuous...
Error estimates of a difference approximation method for a backward heat conduction problem.
Error estimates of a fully discrete linear approximation scheme for Stefan problem.
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 on homogenization of free boundary velocities in periodic media
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 of pseudospectral method for solving the barotropic vorticity equation.
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....