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6 Adaptive Methods

(See exercise 8.)

We stated in the introduction that one of the goals of the modeler is to accurately approximate the solution of bioelectric field problems using a numerical technique. We have discussed how one formulates the problem, discretizes the geometry, and finds an approximate solution. We are now faced with answering the question posed in the problem above pertaining to the accuracy of our solution. To give yourself an intuitive feel for the problem (and possible solution), consider the approximation of a two-dimensional region discretized into triangular elements. We'll apply the finite element method to solve Laplace's equation in the region.