Assessment of Nitsche’s Method for Dirichlet Boundary Conditions Treatment

Approximate Dirichlet Boundary Conditions in the Generalized Finite Element Method

We propose a method for treating the Dirichlet boundary conditions in the framework of the Generalized Finite Element Method (GFEM). We use approximate Dirichlet boundary conditions as in [12] and polynomial approximations of the boundary. Our sequence of GFEM-spaces considered, Sμ, μ = 1, 2, . . . is such that Sμ 6 ⊂ H1 0 (Ω), and hence it does not conform to one of the basic FEM conditions. L...

The Fictitious Boundary Method for the implicit treatment of Dirichlet boundary conditions with applications to incompressible flow simulations

A 'fictitious boundary method' for computing incompressible flows with complicated small-scale and/or time-dependent geometric details is presented. The underlying technique is based on a special treatment of Dirichlet boundary conditions , particularly for FEM discretizations, together with so-called 'iterative filtering techniques' in the context of hierarchical multigrid approaches such that...

Absorption semigroups and dirichlet boundary conditions

TECHNISCHE UNIVERSITÄT BERLIN Moving Dirichlet Boundary Conditions

This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet bound...

Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions

when ε ≥ 0 is small. In particular, ∆2v + εv ≥ 0 in Ω, with v = ∆v = 0 on ∂Ω, implies v ≥ 0 for ε small. In numerical experiments ([14]) for one dimension a similar behaviour was observed under Dirichlet boundary conditions v = ∂ ∂nv = 0. In this paper we will derive a 3-G type theorem as in (1) but with G1,n replaced by the Green function Gm,n for the m-polyharmonic operator with Dirichlet bou...