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Erik Burman

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Related publications (25)

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A Domain Decomposition Method Based on Weighted Interior Penalties for Advection-Diffusion-Reaction Problems

Erik Burman, Paolo Zunino

We propose a domain decomposition method for advection-diffusion- reaction equations based on Nitsche's transmission conditions. The advection-dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over ...

2006

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

A unified stabilized method for Stokes' and Darcy's equations

Erik Burman

We use the lowest possible approximation order, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Stokes equation and Darcy's equation, applying an edge stabilization term to avoid locking. We prove that the f ...

2007

Two mixed finite element formulations for the weak imposition of the Neumann boundary conditions for the Darcy flow

Erik Burman, Riccardo Puppi

We propose two different discrete formulations for the weak imposition of the Neumann boundary conditions of the Darcy flow. The Raviart-Thomas mixed finite element on both triangular and quadrilateral meshes is considered for both methods. One is a consis ...

Walter De Gruyter2021

On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws

Erik Burman

A finite element method for Burgers' equation is studied. The method is analyzed using techniques from stabilized finite element methods and convergence to entropy solutions is proven under certain hypotheses on the artificial viscosity. In particular we a ...

Springer Netherlands2007

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 projection stabilization for the Oseen problem and its interpretation as a variational multiscale method

Erik Burman

We propose to apply the recently introduced local projection stabilization to the numerical computation of the Oseen equation at high Reynolds number. The discretization is done by nested finite element spaces. Using a priori error estimation techniques, w ...

2006

Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements

Erik Burman

We propose a stabilized mixed finite element method based on the Scott-Vogelius element tor the Oseen equation. Here. only convection has to he stabilized since by construction both the discrete pressure and the divergence of the discrete velocities, are c ...

2008

A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty

Erik Burman

We discuss stabilized Galerkin approximations in a new framework, widening the scope from the usual dichotomy of the discontinuous Galerkin method on the one hand and Petrov--Galerkin methods such as the SUPG method on the other. The idea is to use interio ...

2005

Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence

Erik Burman

We analyze a nonlinear shock-capturing scheme for H1-conforming, piecewise-affine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions: a local quasi-uniformity property and the Xu- ...

2005

A stabilized non-conforming finite element method for incompressible flow

Erik Burman

In this paper we extend the recently introduced edge stabilization method to the case of non-conforming finite element approximations of the linearized Navier-Stokes equation. To get stability also in the convective dominated regime we add a term giving

2006

Edge stabilization for the generalized Stokes problem: A continuous interior penalty method

Erik Burman

In this note we introduce and analyze a stabilized finite element method for the generalized Stokes equation. Stability is obtained by adding a least squares penalization of the gradient jumps across element boundaries. The method can be seen as a higher o ...

2006

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

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

A finite element level set method for viscous free-surface flows

Erik Burman, Nicola Parolini

2005

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

Pressure projection Stabilizations for Galerkin approximations of Stokes' and Darcy's problem

Erik Burman

In this study, we consider some recent stabilization techniques for the Stokes' problem and show that they are instances of the framework proposed by Brezzi and Fortin in "A minimal stabilisation procedure for mixed finite element methods" (Numer Math 89, ...

2008

Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem

Erik Burman

We stabilize the nonconforming Crouzeix-Raviart element for the Darcy-Stokes problem with terms motivated by a discontinuous Galerkin approach. Convergence of the method is shown, also in the limit of vanishing viscosity. Finally, some numerical examples v ...

2005

Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems

Erik Burman

Oxford, Oxford University Press2010

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