Local CIP Stabilization for Composite Finite Elements

Monotone local projection stabilization schemes for continuous finite elements

This paper presents a new approach to enforcing discrete maximum principles and/or positivity preservation in continuous piecewise-linear finite element approximations to convection-dominated transport problems. Using a linear first-order advection equation as a model problem, we construct elementlevel bilinear forms associated with first-order artificial diffusion operators and their higher-or...

Finite Elements with Local Projection Stabilization for Incompressible Flow Problems

In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization (LPS). These methods preserve the favourable stability and approximation properties of classical residual-based stabilization (RBS) techniques but avoid the strong coupling of velocity and pressure in the stabilization terms. LPS-methods belo...

Composite Finite Elements for Trabecular Bone Microstructures

Composite Finite Elements and Multigrid Lecture

These lecture notes comprise the talks on composite finite elements and multigrid methods given at the Zürich Summerschool 02. The theory of composite finite elements and various applications have been developed since the end of the ninetieth and reviewed in this paper. Basic knowledge in the theory of finite elements and multigrid methods is required.

Composite Finite Elements for 3D Image Based Computing

We present an algorithmical concept for modeling and simulation with partial differential equations (PDEs) in image based computing where the computational geometry is defined through previously segmented image data. Such problems occur in applications from biology and medicine where the underlying image data has been acquired through e. g. computed tomography (CT), magnetic resonance imaging (...