We introduce a reduced basis method that computes rigorous upper and lower bounds of the energy associated with the infinite-dimensional weak solution of parametrized symmetric coercive partial differential equations with piecewise polynomial forcing and operators that admit decompositions that are affine in functions of parameters. The construction of the upper bound appeals to the standard pr...

This paper is concerned with the hp-version of the finite element method (hp-FEM) to treat a variational inequality that models frictional contact in linear elastostatics. Such an approximation of higher order leads to a nonconforming discretization scheme. We employ Gauss-Lobatto quadrature for the approximation of the nonsmooth frictiontype functional and take the resulting quadrature error i...

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) problem and is presented in a mixed va...

We introduce a reduced basis method that computes rigorous upper and lower bounds of the energy associated with the infinite-dimensional weak solution of parametrized steady symmetric coercive partial differential equations with piecewise polynomial forcing and operators that admit decompositions that are affine in functions of parameters. The construction of the upper bound appeals to the stan...

We consider the scattering of monochromatic electromagnetic waves at a dielectric object with a non-smooth surface. This paper studies the discretization of this problem by means of coupling finite element methods (FEM) and boundary element methods (BEM). Straightforward symmetric coupling as in [R. Hiptmair, Coupling of finite elements and boundary elements in electromagnetic scattering, SIAM ...

There are several numerical integration methods [16] that preserve some of the invariants of an autonomous mechanical system. In [8], T.D. Lee studies the possibility that time can be regarded as a bona fide dynamical variable giving a discrete time formulation of mechanics (see also [9, 10]). From other point of view (integrability aspects) Veselov [19] uses a discretization of the equations o...

In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable, and redundant expansion. The discretiza-tion yields an equivalent nonlinear problem on ℓ2(N), the space of frame coefficients. The discrete problem is then ...

In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach [24, 34, 35], where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and effective variational time discretization of geodesics paths is proposed. This requires to minimize a discrete path energy consisting of a sum of co...

In this thesis structure-preserving time integrators for mechanical systems whose configuration space is a Lie Group are derived from a Hamilton-Pontryagin (HP) variational principle. In addition to its attractive properties for degenerate mechanical systems, the HP viewpoint also affords a practical way to design discrete Lagrangians, which are the cornerstone of variational integration theory...

We prove optimal bounds for the discretization error of geodesic finite elements for variational partial differential equations for functions that map into a nonlinear space. For this we first generalize the well-known Céa lemma to nonlinear function spaces. In a second step we prove optimal interpolation error estimates for pointwise interpolation by geodesic finite elements of arbitrary order...