We investigate a linear two-point boundary value problem whose leading term is a Caputo fractional derivative[...]
For both the Poisson model problem and the Stokes problem in any dimension, we prove that the enriched Crouzeix-Raviart elements are actually identical to the first order Raviart-Thomas elements in the sense that they produce the same d[...]
The concept of a variational formulation is usually attributed to Johann Bernoulli as it is directly linked to the classical Calculus of Variations started by Johann and Jacob Bernoulli and later developed by Euler and Lagrange[...]
In this talk, we will present fast multilevel and adaptive finite element methods for the approximate solution of the discrete problems that arise from the discretization of fractional Laplacian[...]
We investigate multigrid methods for the parameter dependent problems. We construct and analyze multigrid methods from the viewpoint of space decomposition and subspace correction[...]
In this talk, we develop convergence theory for a class of goal-oriented adaptive ﬁnite element (GOFEM) algorithms for second order semilinear elliptic equations[...]
Highly oscillatory integrals have an unwarranted reputation being difficult to solve efficiently. However, such integrals have numerous important applications from signal analysis to laser beam propagations[...]
In this talk, I will give a brief introduction to Numerical Relativity, especially the physical and astrophysical background[...]