Related papers: A posteriori error estimates for hierarchical mixe…
In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state…
We verify functional a posteriori error estimate proposed by S. Repin for a class of obstacle problems. The obstacle problem is formulated as a quadratic minimization problem with constrains equivalently formulated as a variational…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
This paper derives a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem with homogeneous Dirichlet boundary conditions. In particular, the resulting error estimator constitutes an upper bound…
In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general…
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…
We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual…
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…
A posteriori residual and hierarchical upper bounds for the error estimates were proved when solving the hypersingular integral equation on the unit sphere by using the Galerkin method with spherical splines. Based on these a posteriori…
A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Cl\'ement-type approach and the…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…
We develop a novel a posteriori error estimator for the $L^2$ error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization…
This paper investigates an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes, employing the CutFEM method. The main contribution is the a posteriori error analysis based on equilibrated fluxes belonging…
We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the…
We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e., vector-valued mapped…
In this article, we present an overview of different a posteriori error analysis and postprocessing methods proposed in the context of nonlinear eigenvalue problems, e.g. arising inelectronic structure calculations for the calculation of…
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…
Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work, we show a priori rates of convergence of this…