# Finite elements

Wednesday, February 28, 2018 - 3:30pm - 4:20pm

Shawn Walker (Louisiana State University)

We consider the generalized Ericksen model of liquid crystals, which is an energy with 8 independent elastic constants that depends on two order parameters $\mathbf{n}$ (director) and $s$ (variable degree of orientation). We will also discuss the modeling of weak anchoring conditions (both homeotropic and planar), and fully coupled electro-statics with flexo-electric and order-electric effects.

Tuesday, January 16, 2018 - 2:00pm - 2:50pm

Shawn Walker (Louisiana State University)

We present a phase field model for nematic liquid crystal droplets with anisotropic surface tension. Our model couples the Cahn-Hilliard equation to Ericksen's one constant model for liquid crystals with variable degree of orientation. We present a special discretization of the liquid crystal energy that can handle the degenerate elliptic part without regularization. In addition, our discretization uses a mass lumping technique in order to handle the unit length constraint. Discrete minimizers are computed via a discrete gradient flow.

Friday, June 30, 2017 - 10:10am - 11:00am

Johnny Guzman (Brown University)

In recent years there has been an interest in finding finite element spaces that yield divergence free approximation for incompressible flows. One of the original finite elements spaces were provided by Scott and Vogelius. The velocity space consist of continuous vector fields that are piecewise polynomials of degree k and the pressure space consist of piecewise polynomials of degree k-1 (with certain restrictions if singular vertices are present). In 1985, Scott and Vogelius proved that for k greater than or equal to 4 these spaces are inf-sup stable.

Wednesday, April 13, 2011 - 3:15pm - 4:15pm

Joannes Westerink (University of Notre Dame)

Coastal Louisiana and Texas are characterized by tremendous complexity and variability in their geography, topography, bathymetry, continental shelf, estuarine systems, and surface roughness. Hurricane Ike significantly impacted both coastal Texas and Louisiana producing a storm surge of more than 5.3m in eastern Texas and more than 2.2 m in eastern Louisiana (more than 500 km away from the storm landfall location).

Sunday, March 6, 2011 - 1:30pm - 3:00pm

Joseph Teran (University of California, Los Angeles)

Sunday, March 6, 2011 - 10:30am - 12:00pm

Joseph Teran (University of California, Los Angeles)

Elasticity plays a fundamental role in many biomechanics and computer

graphics related problems. I will talk about numerical methods used

for simulating elastic phenomena in soft tissues, skeletal muscles as

well as techniques inspired by imaging for determining elastic

constitutive models. Specifically, I will discuss common difficulties

encountered and my recent algorithm developments to address them. I

will put specific emphasis on applications in computer graphics based

graphics related problems. I will talk about numerical methods used

for simulating elastic phenomena in soft tissues, skeletal muscles as

well as techniques inspired by imaging for determining elastic

constitutive models. Specifically, I will discuss common difficulties

encountered and my recent algorithm developments to address them. I

will put specific emphasis on applications in computer graphics based

Wednesday, January 12, 2011 - 8:30am - 9:30am

Cris Cecka (Stanford University)

We discuss multiple strategies to perform general computations on unstructured grids using a GPU, with specific application to the assembly of systems of equations in finite element methods (FEMs). For each method, we discuss the GPU hardware's limiting resources, optimizations, key data structures, and dependence of the performance with respect to problem size, element size, and GPU hardware generation. These methods are applied to a nonlinear hyperelastic material model to develop a large-scale real-time interactive elastodynamic visualization.

Thursday, December 2, 2010 - 9:45am - 10:30am

Andreas Veeser (Università di Milano)

The quality of a finite element solution hinges in particular on the approximation properties of the finite element space. In the first part of this talk we will consider the approximation of the gradient of a target function by continuous piecewise polynomials over a simplicial, 'shape-regular' mesh and prove the following result: the global best approximation error is equivalent to an appropriate sum in terms of the local best approximation errors on the elements, which do not overlap.

Thursday, October 23, 2014 - 11:00am - 11:30am

Anders Logg (Chalmers University of Technology)

The theory of finite element exterior calculus has enabled the

arrangement of a wide selection of well-known finite elements into a

systematic table: the periodic table of finite elements. Much like the

periodic table of chemical elements which clarifies and explains the

properties of the chemical elements based on their electron structure,

the periodic table of finite elements explains the properties of the

finite elements in terms of their mathematical structure.

In this talk, I will present an overview of the status of

arrangement of a wide selection of well-known finite elements into a

systematic table: the periodic table of finite elements. Much like the

periodic table of chemical elements which clarifies and explains the

properties of the chemical elements based on their electron structure,

the periodic table of finite elements explains the properties of the

finite elements in terms of their mathematical structure.

In this talk, I will present an overview of the status of

Monday, November 29, 2010 - 2:15pm - 3:00pm

Randolph Bank (University of California, San Diego)

We will discuss our on-going investigation of

hp-adaptive finite elements. We will focus on a posteriori

error estimates based on superconvergent derivative recovery.

Besides providing both global error estimates and local

error indicators, this family of error estimates also provides

information that forms the basis of our hp-adaptive refinement

and coarsening strategies. In particular, these a posteriori error

estimates address in a cost efficient and natural way the critical

hp-adaptive finite elements. We will focus on a posteriori

error estimates based on superconvergent derivative recovery.

Besides providing both global error estimates and local

error indicators, this family of error estimates also provides

information that forms the basis of our hp-adaptive refinement

and coarsening strategies. In particular, these a posteriori error

estimates address in a cost efficient and natural way the critical