# Diva intro

### From GHER

In oceanography a typical concern consists in determining a field on a regular grid of positions **r** knowing N;_{d} data in locations **r _{j}**, j=1,..., N;

_{d}. This is called the

*gridding problem*and is useful for many applications such as data analysis, graphical display, forcing or initialization of a model.

DIVA stands for *Data-Interpolating Variational Analysis* and is the implementation of *Variational Inverse Method*. It is designed to solve 2-D differential or variational problems of elliptic type with a finite element method. Its end is to obtain a gridded field from the knowledge of sparse data points.

### Formulation

We are looking for the field which minimizes the variational principle:

with

where

- α
_{0}penalizes the field itself (anomalies), - α
_{1}penalizes gradients (no trends), - α
_{2}penalizes variability (regularization), - ยต penalizes data-analysis misfits (objective).

Without loss of generality we can chose α_{2}=1 (homogeneous function).