This paper addresses the existence and regularity of weak solutions for a fully parabolic model of chemotaxis, with prevention of overcrowding, that …

This paper presents a finite-volume method, together with fully adaptive multi-resolution scheme to obtain spatial adaptation, and a Runge-Kutta-Fehl…

We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, p…

We present an a posteriori estimator of the error in the L^2-norm for the numerical approximation of the Maxwell's eigenvalue problem by means of N\'…

The author wishes to express his gratitude to the anonymous referees, whose suggestions and constructive criticisms led to substantial improvements in the presentation. Moreover, I thank Franco Fagnola and Roberto Quezada for helpful comments.

Applying probabilistic techniques we study regularity properties of quantum master equations (QMEs) in the Lindblad form with unbounded coefficients;…

We introduce a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry. The analysis of the resu…

The paper deals with the a posteriori error analysis of a virtual element method for the Steklov eigenvalue problem. The virtual element method has t…

In this paper we analyze a finite element method for solving a quadratic eigenvalue problem derived from the acoustic vibration problem for a heterog…

We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called directio…

We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymm…

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation …

We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model probl…

This work deals with the numerical solution of the monodomain and bidomain models of electrical activity of myocardial tissue. The bidomain model is …

The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variat…

In this paper, we develop a virtual element method (VEM) of high order to solve the fourth order plate buckling eigenvalue problem on polygonal meshe…

We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on th…

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presente…

We will concern only with a pair of quadratic forms in Rn, and use the notation introduced in Section 2. It seems to be the convexity Dines theorem was conceived once Dines awares the following result, known as (strict) Finsler’s theorem: if

We establish various extensions of the convexity Dines theorem for a (joint-range) pair of inhomogeneous quadratic functions. If convexity fails we d…

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