106 citations · 565 across the 59 of their papers we have counts for
73 papers
Boundary Value Correction for the Boundary Element Method
Erik Burman, Peter Hansbo, Mats G. Larson
We develop a boundary element method for the Laplace equation with Dirichlet boundary conditions in a bounded three-dimensional domain. The method uses flat panels of maximum diame…
Structure-Preserving Augmented Lagrangian Finite Element Methods for Cavitation in Reynolds and Stokes Flows
Peter Hansbo, Mats G. Larson
In this paper we propose augmented Lagrangian finite element methods for cavitation in the Reynolds and Stokes models of lubrication, for which the discrete complementarity conditi…
Normal Equations and Discrete Energy Structures for High-Order Streamline Diffusion
Erik Burman, Peter Hansbo, Mats G. Larson
We analyse fully discrete Streamline Diffusion finite element methods, also known as SUPG methods, for time-dependent first-order systems with skew-symmetric spatial operators. To…
A Barrier-Regularized Symmetric Nitsche Method for the Signorini Problem
Peter Hansbo, Mats G. Larson
We introduce and analyze a barrier-regularized symmetric Nitsche method for the scalar Signorini problem. Applying a logarithmic barrier to the nonnegative slack variable in an aug…
Nonconforming -FE/BE coupling on unstructured meshes based on Nitsche's method
Alexey Chernov, Peter Hansbo, Erik Marc Schetzke
We construct and analyse a -FE/BE coupling on non-matching meshes, based on Nitsche's method. Both the mesh size and the polynomial degree are changed to improve accuracy. Nits…
Cut Finite Element Methods for Convection-Diffusion in Mixed-Dimensional Domains
Erik Burman, Peter Hansbo, Mats G. Larson +2
We develop a cut finite element method (CutFEM) for convection--diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in…
Hybridized Augmented Lagrangian Methods for Contact Problems
Erik Burman, Peter Hansbo, Mats G. Larson
This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformula…
Cut finite element method for divergence free approximation of incompressible flow: a Lagrange multiplier approach
Erik Burman, Peter Hansbo, Mats G. Larson
In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of D…
The augmented Lagrangian method as a framework for stabilised methods in computational mechanics
Erik Burman, Peter Hansbo, Mats G. Larson
In this paper we will review recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier--free stabilised methods…
Extension Operators for Trimmed Spline Spaces
Erik Burman, Peter Hansbo, Mats G. Larson +1
We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree with continuous derivatives. The construction is b…
A simple nonconforming tetrahedral element for the Stokes equations
Peter Hansbo, Mats G. Larson
In this paper we apply a nonconforming rotated bilinear tetrahedral element to the Stokes problem in . We show that the element is stable in combination with a piecew…
On the Design of Locking Free Ghost Penalty Stabilization and the Relation to CutFEM with Discrete Extension
Erik Burman, Peter Hansbo, Mats G. Larson
In this note, we develop a new stabilization mechanism for cut finite element methods that generalizes previous approaches of ghost penalty type in two ways: (1) The quantity that…
A divergence preserving cut finite element method for Darcy flow
Thomas Frachon, Peter Hansbo, Erik Nilsson +1
We study cut finite element discretizations of a Darcy interface problem based on the mixed finite element pairs , . Here is the space of di…
Augmented Lagrangian approach to deriving discontinuous Galerkin methods for nonlinear elasticity problems
Peter Hansbo, Mats G. Larson
We use the augmented Lagrangian formalism to derive discontinuous Galerkin formulations for problems in nonlinear elasticity. In elasticity stress is typically a symmetric function…
Nitsche's Finite Element Method for Model Coupling in Elasticity
Peter Hansbo, Mats G. Larson
We develop a Nitsche finite element method for a model of Euler--Bernoulli beams with axial stiffness embedded in a two--dimensional elastic bulk domain. The beams have their own d…
Error estimates for the Smagorinsky turbulence model: enhanced stability through scale separation and numerical stabilization
Erik Burman, Peter Hansbo, Mats G. Larson
In the present work we show some results on the effect of the Smagorinsky model on the stability of the associated perturbation equation. We show that in the presence of a spectral…
CutFEM Based on Extended Finite Element Spaces
Erik Burman, Peter Hansbo, Mats G. Larson
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equat…
Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension
Erik Burman, Peter Hansbo, Mats G. Larson
In this note we develop a fully explicit cut finite element method for the wave equation. The method is based on using a standard leap frog scheme combined with an extension operat…
Low Regularity Estimates for CutFEM Approximations of an Elliptic Problem with Mixed Boundary Conditions
Erik Burman, Peter Hansbo, Mats G. Larson
We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type whe…
A cut finite element method for a model of pressure in fractured media
Erik Burman, Peter Hansbo, Mats G. Larson
We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and…
Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics
Erik Burman, Snorre Christiansen, Peter Hansbo
In this note we will explore some applications of the recently constructed piecewise affine, -conforming element that fits in a discrete de Rham complex [Christiansen and Hu,…
Augmented Lagrangian Method for Thin Plates with Signorini Boundaries
Erik Burman, Peter Hansbo, Mats G. Larson
We consider -continuous approximations of the Kirchhoff plate problem in combination with a mesh dependent augmented Lagrangian method on a simply supported Signorini boundary…
Cut Bogner-Fox-Schmit Elements for Plates
Erik Burman, Mats G. Larson, Peter Hansbo
We present and analyze a method for thin plates based on cut Bogner-Fox-Schmit elements, which are elements obtained by taking tensor products of Hermite splines. The formula…
Comparison of mechanical conditions in a lower leg model with 5 or 6 tissue types while exposed to prosthetic sockets applying finite element analysis
Sara Kallin, Asim Rashid, Kent Salomonsson +1
Lower limb amputees often suffer skin and tissue problems from using their prosthesis which is a challenging biomechanical problem. The finite element method (FEM) has previously b…