153 citations · 333 across the 25 of their papers we have counts for
5 papers · 1 filter
Partial expansion of a Lipschitz domain and some applications
Jay Gopalakrishnan, Weifeng Qiu
We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the e…
Instability in a generalized Keller-Segel model
Patrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr
We present a generalized Keller-Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant fo…
Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions
Douglas N. Arnold, Richard S. Falk, Jay Gopalakrishnan
We consider the finite element solution of the vector Laplace equation on a domain in two dimensions. For various choices of boundary conditions, it is known that a mixed finite el…
An analysis of the practical DPG method
Jay Gopalakrishnan, Weifeng Qiu
In this work we give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specif…
A locking free hp DPG method for linear elasticity with symmetric stresses
Jamie Bramwell, Leszek Demkowicz, Jay Gopalakrishnan +1
We present two new methods for linear elasticity with simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree…