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.