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Displaying 241 –
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601
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...
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.
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...
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....
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.
...
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...
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...
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...
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...
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...
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:...
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