| Convergence analysis
of a quadrature finite element Galerkin method for a biharmonic problem
Rakhim Aitbayev (New Mexico Tech)
The finite element method (FE) is one of the most widely used
numerical methods for solving partial differential equations.
The method approximates the solution of a boundary value
problem (BVP) by a piecewise-polynomial function, which is a
solution of a finite dimensional analogue of the so-called
variational form of the BVP. To form a corresponding linear
system, one needs to evaluate a large number of integrals.
Replacing these integrals by numerical quadratures, gives
the so-called quadrature finite element Galerkin method.
In this presentation, we approximate a Dirichlet BVP with a
biharmonic equation with a quadrature Galerkin scheme
based on the two-point Gaussian quadrature. We will present
convergence results using two techniques: the standard
approach based on the first Strang lemma and the one based
on the equivalent orthogonal spline collocation formulation.