Related papers: Guaranteed and computable error bounds for approxi…
The Biot problem of poroelasticity is extended by Signorini contact conditions. The resulting Biot contact problem is formulated and analyzed as a two field variational inequality problem of a perturbed saddle point structure. We present an…
We derive a posteriori error estimates for a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation. The a posteriori bound is obtained by a splitting of the equation into a linear stochastic partial…
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that…
We present functional-type a posteriori error estimates in isogeometric analysis. These estimates, derived on functional grounds, provide guaranteed and sharp upper bounds of the exact error in the energy norm. {Moreover, since these…
We derive energy-norm aposteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the first completely rigorous derivation of ZZ…
We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…
In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…
This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains. These estimates provide computable and guaranteed upper and lower…
This paper addresses the local recovery of conservative fluxes and the a posteriori error analysis for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed by means of…
We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order…
This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…
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…
We present residual-based a posteriori error estimates of mixed finite element methods for the three-field formulation of Biot's consolidation model. The error estimator is an upper and lower bound of the space time discretization error up…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the $hp$-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities and/or small time steps. We consider different…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…
We derive a posteriori error estimates in the $L_\infty((0,T];L_\infty(\Omega))$ norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat…