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A stochastic model corresponding to a simplified Hookean dumbbells viscoelastic fluid is considered, the convective terms being disregarded. Existence on a fixed time interval is proved provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem.

- Andrea Bonito, Ricardo H. Nochetto
- SIAM J. Numerical Analysis
- 2010

We analyze an adaptive discontinuous finite element method (ADFEM) for symmetric second order linear elliptic operators. The method is formulated on nonconforming meshes made of simplices or quadrilaterals, with any polynomial degree and in any dimension ≥ 2. We prove that the ADFEM is a contraction for the sum of the energy error and the scaled error… (More)

- Andrea Bonito, Ricardo H. Nochetto, M. Sebastian Pauletti
- J. Comput. Physics
- 2010

We consider geometric biomembranes governed by an L-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler… (More)

- Andrea Bonito, Joseph E. Pasciak
- Math. Comput.
- 2015

We present and study a novel numerical algorithm to approximate the action of T := L where L is a symmetric and positive definite unbounded operator on a Hilbert space H0. The numerical method is based on a representation formula for T in terms of Bochner integrals involving (I + tL) for t ∈ (0,∞). To develop an approximation to T , we introduce a finite… (More)

- Andrea Bonito, Jean-Luc Guermond
- Math. Comput.
- 2011

We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H−α with α ∈ ( 1 2 , 1). The method is shown to be convergent and spectrally correct.

- Andrea Bonito, Marco Picasso, Manuel Laso
- J. Comput. Physics
- 2006

- Andrea Bonito, Ronald A. DeVore, Ricardo H. Nochetto
- SIAM J. Numerical Analysis
- 2013

Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to… (More)

We present a mixed finite element method for a model of the flow in a Hele-Shaw cell of 2-D fluid droplets surrounded by air driven by surface tension and actuated by an electric field. The application of interest regards a micro-fluidic device called ElectroWetting on Dielectric (EWOD). Our analysis first focuses on the time-discrete (continuous in space)… (More)

- Andrea Bonito, Erik Burman
- SIAM J. Scientific Computing
- 2008

In this paper we consider a finite element discretization of the Oldroyd-B model of viscoelastic flows. The method uses standard continuous polynomial finite element spaces for velocities, pressures and stresses. Inf-sup stability and stability for convection-dominated flows are obtained by adding a term penalizing the jump of the solution gradient over… (More)

- Andrea Bonito, Jean-Luc Guermond, Bojan Popov
- Math. Comput.
- 2014

We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. Firstand second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL… (More)