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Displaying 821 –
840 of
2283
We present new a posteriori error estimates for the finite volume approximations
of elliptic problems. They are obtained by applying functional a posteriori
error estimates to natural extensions of the approximate solution and its flux
computed by the finite volume method. The estimates give guaranteed upper bounds
for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and
also in terms of the combined primal-dual norms. It is shown that the estimates
provide sharp upper and...
In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping
(given in terms of a boundary integral operator) to solve linear exterior transmission problems in
the plane. As a model we consider a second order elliptic equation in divergence form coupled with
the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational
formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed, and derive
the...
Systems of parabolic differential equations are studied in the paper. Two a posteriori error estimates for the approximate solution obtained by the finite element method of lines are presented. A statement on the rate of convergence of the approximation of error by estimator to the error is proved.
We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also estimates...
We consider a non-conforming stabilized domain
decomposition technique for
the discretization of the three-dimensional Laplace equation.
The aim is to extend the numerical analysis of residual error indicators to
this model problem. Two formulations of the problem are considered
and the error estimators are studied for both. In the
first one, the error estimator provides upper and lower bounds for
the energy norm of the mortar finite element solution whereas in
the second case, it also estimates...
This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the -norm, independent of the diffusion parameter . The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...
This paper is devoted to the study of a posteriori
error estimates for the scalar nonlinear convection-diffusion-reaction equation
.
The estimates for the error between the exact solution and an upwind finite
volume approximation to the solution are derived in the L1-norm,
independent of the diffusion parameter D.
The resulting a posteriori error estimate is used to define an grid adaptive solution
algorithm for the finite volume scheme. Finally numerical experiments underline
the applicability...
For a nonconforming finite element approximation of an elliptic model problem, we propose a posteriori error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is exploited...
For a nonconforming finite element approximation of an elliptic model
problem, we propose a posteriori error estimates in the energy norm
which use as an additive term the “post-processing error” between
the original nonconforming finite element solution and an easy
computable conforming approximation of that solution.
Thus, for the error analysis, the existing theory from the conforming
case can be used together with some simple additional arguments.
As an essential point, the property is...
We consider the efficient and reliable solution of linear-quadratic optimal control problems governed by parametrized parabolic partial differential equations. To this end, we employ the reduced basis method as a low-dimensional surrogate model to solve the optimal control problem and develop a posteriori error estimation procedures that provide rigorous bounds for the error in the optimal control and the associated cost functional. We show that our approach can be applied to problems involving...
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations – Galerkin projection onto a space spanned by solutions of the governing partial differential equation at selected points in parameter space; (ii) a posteriori error estimation – relaxations of the error-residual equation...
We present a technique for the rapid and reliable prediction of
linear-functional
outputs of elliptic coercive partial differential equations with affine
parameter dependence. The essential components are (i )
(provably) rapidly
convergent global reduced-basis approximations – Galerkin projection
onto a space
WN spanned by solutions of the governing partial differential
equation at N
selected points in parameter space; (ii ) a posteriori
error estimation
– relaxations of the error-residual equation...
We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian....
We derive a posteriori estimates for a discretization in space of the standard
Cahn–Hilliard equation with a double obstacle free energy.
The derived estimates are robust and efficient, and in practice are combined
with a heuristic time step adaptation.
We present numerical experiments in two and three space dimensions and compare
our method with an existing heuristic spatial mesh adaptation algorithm.
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840 of
2283