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This paper is concerned with the derivation of computable and guaranteed upper bounds of the difference between the exact and the approximate solution of an exterior domain boundary value problem for a linear elliptic equation. Our analysis…

Analysis of PDEs · Mathematics 2011-05-23 Dirk Pauly , Sergey Repin

We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…

Numerical Analysis · Mathematics 2014-04-03 Karakatsani Fotini

We suggest guaranteed, robust a posteriori error bounds for approximate solutions of the reaction-diffusion equations, modeled by the equation $-\Delta u+\sigma u= f$ in $\Omega$ with any $\sigma={\mathrm{const}}\ge 0$. We also term our…

Numerical Analysis · Mathematics 2017-11-07 Vadim Glebovich Korneev

We describe a posteriori error analysis for a discontinuous Galerkin method for a fourth order elliptic interface problem that arises from a linearized model of thin sheet folding. The primary contribution is a local efficiency bound for an…

Numerical Analysis · Mathematics 2025-07-02 Harbir Antil , Sean P. Carney , Rohit Khandelwal

In this paper, we prove some a priori estimates for a system of partial differential equations arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The unknowns of…

Analysis of PDEs · Mathematics 2018-07-12 Aníbal Coronel , Enrique Fernández-Cara , Marko Rojas-Medar , Alex Tello

We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…

Optimization and Control · Mathematics 2025-05-26 Francisco Fuica

In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal…

Numerical Analysis · Mathematics 2017-11-16 Immanuel Anjam , Dirk Pauly

We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of…

Numerical Analysis · Mathematics 2024-12-20 Luca Ratti , Marco Verani

Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…

Numerical Analysis · Mathematics 2023-02-01 Zhengqi Zhang , Zhi Zhou

We present a localized a-posteriori error estimate for the localized reduced basis multi-scale (LRBMS) method [Albrecht, Haasdonk, Kaulmann, Ohlberger (2012): The localized reduced basis multiscale method]. The LRBMS is a combination of…

Numerical Analysis · Mathematics 2019-10-30 Mario Ohlberger , Felix Schindler

We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…

Numerical Analysis · Mathematics 2018-06-14 Francisco Fuica , Enrique Otarola , Abner J. Salgado

In two and three dimensional Lipschitz, but not necessarily convex, polytopal domains, we propose and analyze a posteriori error estimators for an optimal control problem involving the stationary Navier--Stokes equations; control…

Numerical Analysis · Mathematics 2021-01-13 Alejandro Allendes , Francisco Fuica , Enrique Otarola , Daniel Quero

We propose a method of obtaining a posteriori estimates which does not use the duality theory and which applies to variational inequalities with monotone operators, without assuming the potentiality of operators. The effectiveness of the…

Analysis of PDEs · Mathematics 2025-04-15 Vladimir Bobkov , Svetlana Pastukhova

We give stationary estimates for the derivative of the expectation of a non-smooth function of bounded variation f of the workload in a G/G/1/$\infty$ queue, with respect to a parameter influencing the distribu- tion of the input process.…

Probability · Mathematics 2012-07-16 Pierre Bremaud , Jean-Marc Lasgouttes

This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…

Numerical Analysis · Mathematics 2025-08-27 Markus Bachmayr , Simon Boisserée

A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…

Mathematical Physics · Physics 2012-09-24 James Q. Feng

Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

Numerical Analysis · Mathematics 2026-05-12 T. Catoe , V. J. Ervin

This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…

Econometrics · Economics 2024-11-04 Donald W. K. Andrews , Ming Li

We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…

Numerical Analysis · Mathematics 2020-03-23 Bernhard Endtmayer , Ulrich Langer , Thomas Wick

We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…

Distributed, Parallel, and Cluster Computing · Computer Science 2008-04-12 S. Sundhar Ram , V. V. Veeravalli , A. Nedic