54 research outputs found
Gradient Schemes for Linear and Non-linear Elasticity Equations
The Gradient Scheme framework provides a unified analysis setting for many
different families of numerical methods for diffusion equations. We show in
this paper that the Gradient Scheme framework can be adapted to elasticity
equations, and provides error estimates for linear elasticity and convergence
results for non-linear elasticity. We also establish that several classical and
modern numerical methods for elasticity are embedded in the Gradient Scheme
framework, which allows us to obtain convergence results for these methods in
cases where the solution does not satisfy the full -regularity or for
non-linear models
Application of projection algorithms to differential equations: boundary value problems
The Douglas-Rachford method has been employed successfully to solve many
kinds of non-convex feasibility problems. In particular, recent research has
shown surprising stability for the method when it is applied to finding the
intersections of hypersurfaces. Motivated by these discoveries, we reformulate
a second order boundary valued problem (BVP) as a feasibility problem where the
sets are hypersurfaces. We show that such a problem may always be reformulated
as a feasibility problem on no more than three sets and is well-suited to
parallelization. We explore the stability of the method by applying it to
several examples of BVPs, including cases where the traditional Newton's method
fails
A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D
Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as multigrid methods can be easily adapted to the nonconforming situation. We present the discretization errors in different norms for linear and quadratic mortar finite elements with different Lagrange multiplier spaces. Numerical results illustrate the performance of our approach
- …