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Displaying 61 –
80 of
601
Motivated by the pricing of American options for baskets we
consider a parabolic variational inequality in a bounded
polyhedral domain with a continuous piecewise
smooth obstacle. We formulate a fully discrete method by using
piecewise linear finite elements in space and the backward Euler
method in time. We define an a posteriori error estimator and show
that it gives an upper bound for the error in
L2(0,T;H1(Ω)). The error estimator is localized in the
sense that the size of the elliptic residual...
The time-dependent Stokes equations in two- or three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.
The time-dependent Stokes equations in two- or three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.
We derive a residual-based a posteriori error estimator for a discontinuous Galerkin approximation of the Steklov eigenvalue problem. Moreover, we prove the reliability and efficiency of the error estimator. Numerical results are provided to verify our theoretical findings.
The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in , or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main results...
The paper presents an a posteriori error estimator for a (piecewise linear)
nonconforming finite element approximation of the heat equation
in , d=2 or 3,
using backward Euler's scheme.
For this discretization, we derive a residual indicator, which use
a spatial residual indicator based on the
jumps of normal and tangential derivatives of the nonconforming
approximation and
a time residual indicator based on the jump of broken gradients at each time step.
Lower and
upper bounds form the main...
In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt’s class A2. The theory hinges on local approximation properties of either Clément or Scott–Zhang interpolation...
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...
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...
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 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...
Currently displaying 61 –
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601