We consider the identification of nonlinear diffusion coeficients of the form a(t;u) or a(u) in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assu...
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The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical cont...
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Two-dimensional Kelvin–Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considera...
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This work introduces a parallel and rank-adaptive matrix integrator for dynamical low-rank approximation. The method is related to the previously proposed rank-adaptive basis update & Galerkin (BUG) integrator but...
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We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains sharing a common interface. The PDEs...
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Background: Perivascular fluid flow, of cerebrospinal or interstitial fluid in spaces surrounding brain blood vessels, is recognized as a key component underlying brain transport and clearance. An important open quest...
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We provide a MATLAB package p1afem for an adaptive P1-finite element method (AFEM). This includes functions for the assembly of the data, different error estimators, and an indicator-based adaptive mesh-refining algor...
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We present an equilibration-based a posteriori error estimator for Nédélec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient correction to the estimator for...
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Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to studying the convergence of the finit...
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In this paper we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components of the metric tensor are assumed to b...
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