Error Estimates for Galerkin Methods for Quasilinear Parabolic and Elliptic Differential Equations in Divergence Form.
Error estimates for least-squares mixed finite elements
Error estimates for linear finite elements on Bakhvalov-type meshes
For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh.
Error Estimates for MAC-Like Approximations to the Linear Navier-Stokes Equations.
Error estimates for mixed methods
Error estimates for modified local Shepard’s formulas in Sobolev spaces
Interest in meshfree methods in solving boundary-value problems has grown rapidly in recent years. A meshless method that has attracted considerable interest in the community of computational mechanics is built around the idea of modified local Shepard’s partition of unity. For these kinds of applications it is fundamental to analyze the order of the approximation in the context of Sobolev spaces. In this paper, we study two different techniques for building modified local Shepard’s formulas, and...
Error estimates for Modified Local Shepard's Formulas in Sobolev spaces
Interest in meshfree methods in solving boundary-value problems has grown rapidly in recent years. A meshless method that has attracted considerable interest in the community of computational mechanics is built around the idea of modified local Shepard's partition of unity. For these kinds of applications it is fundamental to analyze the order of the approximation in the context of Sobolev spaces. In this paper, we study two different techniques for building modified local Shepard's formulas, and...
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 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 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 solutions of variational inequalities.
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 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...