A conservative variational method for multicomponent concentration time dependent diffusion (Q1821530)

The multicomponent time-dependent linear diffusion-decay equation with diagonal space-dependent diffusion matrix and source-term is considered in a one-dimensional bounded spatial interval, whose coordinate may be cartesian, plane-radial or spherical. The equation is replaced by a variational formulation from which by subdivision of the interval in cells, taking a cubic polynomial as trial function in each cell, imposing appropriate inter-cell-continuity conditions and conditions on the boundary, a discretized version is obtained. In general, this discretization is not conservative. Cell-wise conservation is restored by additional constraints which are incorporated by the Lagrange multiplier technique. The resulting system of ordinary differential equations is treated numerically by an exponential matrix method. The results of extensive numerical case studies are documented; they exhibit high accuracy and stress the importance and usefulness of taking of conservativity.