Peter Hansbo
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View article: Cut finite element methods
Cut finite element methods Open
Cut finite element methods (CutFEM) extend the standard finite element method to unfitted meshes, enabling the accurate resolution of domain boundaries and interfaces without requiring the mesh to conform to them. This approach preserves t…
View article: Hybridized Augmented Lagrangian Methods for Contact Problems
Hybridized Augmented Lagrangian Methods for Contact Problems Open
This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformulating the contact problem as a nonlinear variational equalit…
A simple nonconforming tetrahedral element for the Stokes equations Open
In this paper we apply a nonconforming rotated bilinear tetrahedral element to the Stokes problem in $\mathbb{R}^3$. We show that the element is stable in combination with a piecewise linear, continuous, approximation of the pressure. This…
Cut finite element method for divergence free approximation of incompressible flow: a Lagrange multiplier approach Open
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 Dirichlet boundary conditions we consider either Nitsche's m…
The augmented Lagrangian method as a framework for stabilised methods in computational mechanics Open
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. We first show how the method generates Galerkin/Least Squ…
A divergence preserving cut finite element method for Darcy flow Open
We study cut finite element discretizations of a Darcy interface problem based on the mixed finite element pairs $\textbf{RT}_k\times Q_k$, $k\geq 0$. Here $Q_k$ is the space of discontinuous polynomial functions of degree less or equal to…
Augmented Lagrangian approach to deriving discontinuous Galerkin methods for nonlinear elasticity problems Open
We use the augmented Lagrangian formalism to derive discontinuous Galerkin (DG) formulations for problems in nonlinear elasticity. In elasticity, stress is typically a symmetric function of strain, leading to symmetric tangent stiffness ma…
On the Design of Locking Free Ghost Penalty Stabilization and the Relation to CutFEM with Discrete Extension Open
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 is stabilized and (2) The choice of elements that are conne…
Augmented Lagrangian approach to deriving discontinuous Galerkin methods for nonlinear elasticity problems Open
We use the augmented Lagrangian formalism to derive discontinuous Galerkin formulations for problems in nonlinear elasticity. In elasticity stress is typically a symmetric function of strain, leading to symmetric tangent stiffness matrices…
Error Estimates for the Smagorinsky Turbulence Model: Enhanced Stability Through Scale Separation and Numerical Stabilization Open
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 gap, such that the flow can be decomposed in a large scale…
CutFEM Based on Extended Finite Element Spaces Open
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersecte…
Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension Open
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 operator that defines the nodal values outside of the domain in t…
Low Regularity Estimates for CutFEM Approximations of an Elliptic Problem with Mixed Boundary Conditions Open
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 where we consider the case when the exact solution $u \in H^s$…
Comparison of mechanical conditions in a lower leg model with 5 or 6 tissue types while exposed to prosthetic sockets applying finite element analysis Open
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 been applied to analyse internal mechanical conditions of th…
Analysis of finite element methods for vector Laplacians on surfaces Open
We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in ${\mathbb{R}}^3$. Closely related operators arise in models of flow on surfaces as well as el…