Error estimates for some quasi-interpolation operators
Error estimates for some quasi-interpolation operators
We derive explicit bounds on the constants in error estimates for two quasi-interpolation operators which are modifications of the “classical” Clément-operator. These estimates are crucial for making explicit the constants which appear in popular a posteriori error estimates. They are also compared with corresponding estimates for the standard nodal interpolation operator.
Error Estimates for Spline Interpolants on Equidistant Grids.
Error estimates for the approximation of some unilateral problems
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 approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.
Error Estimates for the Finite Element Solution of Variational Inequalities. Part I. Primal Theory.
Error Estimates for the Finite Element Solution of Variational Inequalities. Part II. Mixed Methods.
Error estimates for the finite element solutions of variational inequalities.
Error estimates for the finite element solutions of variational inequalities
Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints
Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints
The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states....
Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints
The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states. ...
Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations.
Error estimates for the ultra weak variational formulation in linear elasticity
We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L2(Ω) norm in terms of the best approximation...
Error estimates for the ultra weak variational formulation in linear elasticity∗
We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate...
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.