We study a family of $ H^ m $-conforming piecewise polynomials based on artificial neural
network, named as the finite neuron method (FNM), for numerical solution of $2 m $-th order …

In this work, we exploit the capability of virtual element methods in accommodating
approximation spaces featuring high-order continuity to numerically approximate differential …

Since the nonconforming P1 finite element method for the Stokes equations was introduced
by M. Crouzeix and PA Raviart in 1973, there have been many advances in the finite …

We investigate a quadratic C^ 0 C 0 interior penalty method for the approximation of isolated
solutions of a von Kármán plate. We prove that the discrete problem is uniquely solvable …

We present a class of spline finite element methods for time-domain wave propagation
which are particularly amenable to explicit time-stepping. The proposed methods utilize a …

In this paper, we propose a family of nonconforming finite elements for $2 m $ th order
partial differential equations in $\mathbb {R}^ n $ on simplicial grids when $ m= n+ 1$. This …

The H^ m H m-nonconforming virtual elements of any order k on any shape of polytope in R^
n R n with constraints m> nm> n and k ≥ mk≥ m are constructed in a universal way. A …

In this chapter we review recent results on the conforming virtual element approximation of
polyharmonic and eleastodynamics problems. The structure and the content of this review is …

A stable splitting of $2 m $-th order elliptic partial differential equations into $2 (m-1) $
problems of Poisson type and one generalized Stokes problem is established for any space …

In this work we will present a method of virtual elements to approximate the solution of a
polyharmonic problem (− Δ) nu= g. We will consider m+ 1 auxiliary unknowns when n= 2 m+ …