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Could someone give me some reference to the Numerical solution of a System of PDEs of following type.. (which also encompasses strongly elliptic system of PDEs) in 2D or 3D.

$$\left\{ \begin{aligned} & \mathrm{div} (\mathbf{U}_k)=f_k , \text{ for } k=1,\ldots,M \\ &\mathbf{U}_k = \sum^M_{l=1}B_{kl} \cdot \mathrm{grad\,} P_l ,\text{ for } k=1,\ldots,M \end{aligned}\right. $$

where $B_{kl}$ is a matrix of appropriate dimension.

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