Mathematical Sciences Department Colloquium - Mark Ainsworth, Brown University

Mathematical Sciences Department

Colloquium

Speaker: Mark Ainsworth, Brown University

Friday, April 26, 2024

11am-12pm

Salisbury Labs 105

Title: High order mixed finite element approximation of incompressible flow

Abstract: There are 100s of mixed finite element schemes for incompressible going back over nearly five decades, but the search continues. In this talk, we highlight the main challenges in developing mixed finite elements with a particular emphasis on high order elements and explain why the task has proved so troublesome. We show how ideas from algebraic topology are relevant to the problem and how we have used them in our work to construct high order mixed finite elements on triangular meshes that conserve mass, are pressure robust, are uniformly inf-sup stable in both the mesh-size and the polynomial degree and deliver exponential rates of convergence. The implementation and preconditioning of the elements will also be briefly mentioned. This is based on work with Charles Parker (Oxford, ex Brown).