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Over the last decade, finite volume discretizations for flow in porous media have been extended to handle situations where fractures dominate the flow. These discretizations have successfully been combined with the discrete fracture-matrix…

Numerical Analysis · Mathematics 2017-12-25 Ivar Stefansson , Inga Berre , Eirik Keilegavlen

We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…

Optimization and Control · Mathematics 2022-03-31 Francisco Fuica , Enrique Otarola

In this work we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in…

Numerical Analysis · Mathematics 2020-04-23 Koffi Wilfrid Houédanou

In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…

Numerical Analysis · Mathematics 2026-02-03 Ani Miraçi , Jan Papež , Martin Vohralík , Ivan Yotov

We consider primal-dual mixed finite element methods for the solution of the elliptic Cauchy problem, or other related data assimilation problems. The method has a local conservation property. We derive a priori error estimates using known…

Numerical Analysis · Mathematics 2018-01-01 Erik Burman , Mats. G. Larson , Lauri Oksanen

Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids subject to external magnetic fields, e.g. plasmas and liquid metals. The efficient and robust solution of the MHD system poses many challenges due to it's…

Numerical Analysis · Mathematics 2020-12-18 J. H. Chaudhry , A. E. Rappaport , J. N. Shadid

We present a dual weighted residual-based a posteriori error estimate for a discontinuous Galerkin (DG) approximation of a linear second-order elliptic problem on compact smooth connected and oriented surfaces in $\mathbb{R}^{3}$ which are…

Numerical Analysis · Mathematics 2014-02-11 Andreas Dedner , Pravin Madhavan

Elliptic reconstruction property, originally introduced by Makridakis and Nochetto for linear parabolic problems, is a well-known tool to derive optimal a posteriori error estimates. No such results are known for nonlinear and nonsmooth…

Numerical Analysis · Mathematics 2024-05-29 Harbir Antil , Rohit Khandelwal

This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…

Numerical Analysis · Mathematics 2016-11-23 E. H. van Brummelen , S. Zhuk , G. J. van Zwieten

In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…

Numerical Analysis · Mathematics 2020-08-21 Fernando A Morales

This paper introduces an explicit residual-based a posteriori error analysis for the symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise symmetric and H(div)-conforming stress approximation.…

Numerical Analysis · Mathematics 2017-05-25 C. Carstensen , D. Gallistl , J. Gedicke

We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…

Machine Learning · Computer Science 2026-02-23 Rajneil Baruah

In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes [Jha20.CAMWA] to the newly proposed algebraic stabilization schemes…

Numerical Analysis · Mathematics 2024-04-04 Abhinav Jha

We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…

Numerical Analysis · Mathematics 2024-04-29 Alexandre L. Madureira , Marcus Sarkis

We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra time-regularity for the…

Numerical Analysis · Mathematics 2024-12-23 T. Chaumont-Frelet , A. Ern

We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the…

Numerical Analysis · Mathematics 2021-08-27 Blanca Ayuso de Dios , Thirupathi Gudi , Kamana Porwal

Post-processing techniques are essential tools for enhancing the accuracy of finite element approximations and achieving superconvergence. Among these, recovery techniques stand out as vital methods, playing significant roles in both…

Numerical Analysis · Mathematics 2024-12-06 Hailong Guo , Zhimin Zhang

We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…

Numerical Analysis · Mathematics 2015-07-30 Fernando D. Gaspoz , Pedro Morin , Andreas Veeser

We provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on the angular momentum formulation. Our analysis is based on novel weak-strong stability estimates which…

Numerical Analysis · Mathematics 2023-07-25 Jan Giesselmann , Elena Mäder-Baumdicker , David Jakob Stonner

We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes…

Numerical Analysis · Mathematics 2020-05-13 Andrea Cangiani , Emmanuil H. Georgoulis , Oliver J. Sutton