Approximating the total variation with finite differences or finite elements

Mesh-Centered Finite Differences from Nodal Finite Elements

After it is shown that the classical ve points mesh-centered nite diierence scheme can be derived from a low order nodal nite element scheme by using nonstandard quadrature formulae, higher order block mesh-centered nite diierence schemes for second-order elliptic problems are derived from higher order nodal nite elements with nonstandard quadrature formulae as before, combined to a procedure k...

Finite differences and finite elements: getting to know you

T o debug your programs, it’s helpful to experiment with the simplest test problem and a small number of mesh points. Look ahead to Problem 6 for sample problems. Problem 2 uses the Matlab function spdiags to construct a sparse matrix. If you have never used sparse matrices in Matlab, print the matrix A to see that its data structure contains the row index, column index, and value for each nonz...

On the Displacement-Stress Continuous Finite Elements

For the analysis of composite media, three different compatible and mixed finite element formulations are presented which apriori enforce the continuity of stresses as well as displacements at the element interfaces. The formulations are applied for the analysis of hi-material interfaces in two problems often encountered in the field of orthopaedic biomechanics, that is the fixation analysis in...

Mixed Finite Elements for Elliptic Problems with Tensor Coeecients as Cell-centered Finite Diierences Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-centered Finite Differences

We present an expanded mixed nite element approximation of second order elliptic problems containing a tensor coeecient. The mixed method is expanded in the sense that three variables are explicitly approximated, namely, the scalar unknown, the negative of its gradient, and its ux (the tensor coeecient times the negative gradient). The resulting linear system is a saddle point problem. In the c...

Mixed Finite Elements as Finite Differences for Elliptic Equations on Triangular Elements