This paper is concerned with the generalization of the finite element method via the use of
non-polynomial enrichment functions. Several methods employ this general approach, eg …

Let Γ be a smooth curve inside a two-dimensional rectangular region Ω. In this paper, we
consider the Poisson interface problem−∇ 2 u= f in Ω∖ Γ with Dirichlet boundary condition …

In this work, we develop variational formulations of Petrov--Galerkin type for one-
dimensional fractional boundary value problems involving either a Riemann--Liouville or …

Physics-informed neural networks (PINNs) are a powerful class of numerical solvers for
partial differential equations, employing deep neural networks with successful applications …

In this work, we develop an efficient solver based on neural networks for second-order
elliptic equations with variable coefficients and a singular source. This class of problems …

We consider a boundary value problem involving a Riemann–Liouville fractional derivative
of order α∈(3/2, 2) on the unit interval (0, 1). The standard Galerkin finite element …

The excitonic luminescence of a highly ordered single conjugated polymer chain is studied
by microphotoluminescence. At T≤ 10 K it consists of a single Lorentzian line. The linewidth …

It is shown in Choi and Kweon (2013) that a solution of the Navier–Stokes equations with no-
slip boundary condition on a non-convex polygon can be written as [u, p]= C 1 [Φ 1, ϕ 1]+ C …

Let [Formula: see text] be the distance function to the origin O∈ R2, and let us fix δ> 0. We
consider the “Schrödinger-type mixed boundary value problem”− Δu+ δr− 2u= f∈ Hm− 1 (Ω) …

It is well known that the regularity of solutions of elliptic partial differential equations on
domains with re-entrant corners is limited by the maximal interior angle. This results in …