Preprint B10/2005
The Weighted Extended B-Splines Finite Element Method

Martha Sofia Miranda

**Keywords: **
Finite elements method | uniform B-splines

When using the finite element method based on domain dependent grids to solve
numerically
elliptic partial differential equations with Dirichlet boundary condition,
we have to consider that constructing and refining appropriate grids
and triangulations are not an easy task, specially in dimensions $m >2$.
This difficulty can be overcame by using domain independent uniform grids,
B-splines and related objects, such as finite element basis functions.
In this monography, we present the main properties of uniform B-splines,
uniform weighted B-splines and uniform weighted extended B-splines
when used as finite element spaces to solve elliptic partial equation
with Dirichlet boundary conditions. We include the error analysis using best
approximation estimates.