Jay Gopalakrishnan

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A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion(More)
We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifi­ cally, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a "trial-to-test" operator T, which(More)
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 element method, in which the rotation of the solution is introduced as a second unknown, is advantageous, and appropriate choices of mixed finite element spaces lead to a stable,(More)
The recent Zika virus (ZIKV) epidemic is associated with microcephaly in newborns. Although the connection between ZIKV and neurodevelopmental defects is widely recognized, the underlying mechanisms are poorly understood. Here we show that two recently isolated strains of ZIKV, an American strain from an infected fetal brain (FB-GWUH-2016) and a(More)
Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using “broken” test spaces, i.e., spaces of functions with no continuity constraints across mesh element interfaces. Broken spaces derivable from a standard exact sequence of first order (unbroken) Sobolev spaces are of particular interest. A characterization of interface spaces that(More)
A mutation in the centrosomal-P4.1-associated protein (CPAP) causes Seckel syndrome with microcephaly, which is suggested to arise from a decline in neural progenitor cells (NPCs) during development. However, mechanisms ofNPCs maintenance remain unclear. Here, we report an unexpected role for the cilium inNPCs maintenance and identifyCPAPas a negative(More)
Stem cells are characterized by their ability to asymmetrically divide, generating another self-renewing stem cell and a differentiating daughter cell. They reside within the local niche microenvironment, which, together with systemic signals, regulates intrinsic stem cell function. Stem cells are finely regulated, with even slight deregulation leading to(More)
The article reviews fundamentals of Discontinuous Petrov-Galerkin (DPG) Method with Optimal Test Functions. The main idea admits three different interpretations: a Petrov-Galerkin method with (optimal) test functions that realize the supremum in the inf-sup condition, a minimumresidual method with residual measured in a dual norm, and a mixed formulation(More)
Although small-molecule drug discovery efforts have focused largely on enzyme, receptor, and ion-channel targets, there has been an increase in such activities to search for protein-protein interaction (PPI) disruptors by applying high-throughout screening (HTS)-compatible protein-binding assays. However, a disadvantage of these assays is that many primary(More)
We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous PetrovGalerkin (DPG) framework. In this framework, both the stress and the displacement approximations are(More)