Analysis, Dynamics and Applications Seminar

The finite volume Laplacian is a particular type of weighted graph Laplacian on a triangulation in which the weights are determined by a geometric dual structure. Finite volume methods may be used to numerically approximate PDEs. In dimension two, finite element Laplacians may be viewed as a special case of the finite volume Laplacian. In addition, when considering variations of discrete conformal structures, the derivative of the vertex curvature can be expressed as a finite volume Laplacian. Because the weights for the finite volume Laplacian may be negative, in general its definiteness is not guaranteed. However, its determinant in any dimension is related to the signed volume of a certain simplex determined by the original simplex and duality structure.

Speaker will be in-person.