Karl Larsson

A continuous/discontinuous Galerkin method and a priori error estimates for the biharmonic problem on surfaces

We present a continuous/discontinuous Galerkin method for approximating solutions to a fourth order elliptic PDE on a surface embedded in R-3. A priori error estimates, taking both the approximatio ...

Variational formulation of curved beams in global coordinates

In this paper we derive a variational formulation for the static analysis of a linear curved beam natively expressed in global Cartesian coordinates. Using an implicit description of the beam midline during derivation we eliminate the need for local coordinates. The only geometrical information appearing in the final expressions for the governing equations is the tangential direction. As a consequence, zero or discontinuous curvature, for example at inflection points, pose no difficulty in this formulation. Kinematic assumptions encompassing both Timoshenko and Euler–Bernoulli beam theories are considered. With the exception of truly three-dimensional formulations, models for curved beams found in the literature are typically derived in the local Frenet frame. We implement finite element methods with global degrees of freedom and discuss curvature coupling effects and locking. Numerical comparisons with classical solutions for straight and curved cantilever beams under tip load are given, as well as numerical examples illustrating curvature coupling effects.

Shape optimization using the cut finite element method

We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by ...

Finite element approximation of the Laplace–Beltrami operator on a surface with boundary

We develop a finite element method for the Laplace–Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche’s method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order

A Nitsche method for elliptic problems on composite surfaces

k \ge 1

Cut finite elements for convection in fractured domains

k≥1 in the energy and

Continuous piecewise linear finite elements for the Kirchhoff–Love plate equation

L^2