Finite elements

High-order non-conforming finite elements for the Stokes equation

Stefan Sauter, Professor, Institute of Mathematics, University of Zurich

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B2 L5 R5220

We consider non-conforming discretizations of the stationary Stokes equation in two and three dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit and also contains substantial freedom for a concrete choice.

Finite element approximations for variable-order fractional diffusion problems

Prof. Wenyu Lei, University of Electronic Science and Technology of China

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B4 L5 R5209

We propose a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. A number of challenges are encountered when discretizing such problems. The first is the heterogeneous kernel singularity in the fractional integral operator. The second comes from the dense discrete operator with its quadratic growth in memory footprint and arithmetic operations. To address these challenges, we propose a strategy that decomposes the system matrix into three components. The first is a sparse matrix that handles the singular near-field separately and is computed by adapting singular quadrature techniques available for the homogeneous case to the case of spatially variable order.

Rolf Krause

Professor Rolf Krause is an experienced researcher and educator specializing in designing and analyzing algorithms to solve complex problems in scientific computing and machine learning.

Daniele Boffi

Professor Boffi is a leading international expert in mixed finite elements and the approximation of eigenvalue problems arising from partial differential equations.