Publications de Benjamin Stamm

Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods

We propose two new and enhanced algorithms for greedy sampling of high- dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the devel- opment ...

EDP Sciences2014

Interior penalty continuous and discontinuous finite element approximations of hyperbolic equations

Alfio Quarteroni, Erik Burman, Benjamin Stamm

In this paper we present the continuous and discontinuous Galerkin methods in a unified setting for the numerical approximation of the transport dominated advection-reaction equation. Both methods are stabilized by the interior penalty method, more precise ...

2010

Local discontinuous Galerkin method for diffusion equations with reduced stabilization

Erik Burman, Benjamin Stamm

We extend the results on minimal stabilization of Burman and Stamm[J. Sci. Comp., 33 (2007), pp. 183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the poly ...

2009

Stabilization strategies for discontinuous Galerkin methods

Benjamin Stamm

The subject of this thesis is the analysis of discontinuous Galerkin methods for linear partial differential equations of first or second order. Discontinuous Galerkin methods are known to satisfy a local mass conservation property. Taking a closer look on ...

EPFL2008

Low order discontinuous Galerkin methods for second order elliptic problems

Erik Burman, Benjamin Stamm

We consider DG-methods for 2nd order scalar elliptic problems using piecewise aﬃne approximation in two or three space dimensions. We prove that both the symmetric and the non-symmetric version of the DG-method have regular system matrices also without pen ...

2008

Symmetric and non-symmetric discontinuous Galerkin methods stabilized using bubble enrichment

Erik Burman, Benjamin Stamm

In this Note we prove that in two and three space dimensions, the symmetric and non-symmetric discontinuous Galerkin method for second order elliptic problems is stable when using piecewise linear elements enriched with quadratic bubbles without any penali ...

2008

Stabilization strategies for high order methods for transport dominated problems

Alfio Quarteroni, Erik Burman, Benjamin Stamm

Standard high order Galerkin methods, such as pure spectral or high order finite element methods, have insufficient stability properties when applied to transport dominated problems. In this paper we review some stabilization strategies for pure spectral m ...

2008

Minimal stabilization of discontinuous Galerkin finite element methods for hyperbolic problems

Erik Burman, Benjamin Stamm

We consider a discontinuous Galerkin finite element method for the advection– reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained ...

2007

The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders p ≥ 2

Erik Burman, Benjamin Stamm

In this Note we prove that in one space dimension, the symmetric discontinuous Galerkin method for second order elliptic problems is stable for polynomial orders

p \ge 2

without using any stabilization parameter. The method yields optimal convergence rat ...

2007