Abstract
AbstractWe consider an example of a boundary value problem on an interval where the solution can show strong oscillations. In order to solve such a problem numerically, standard methods require meshes that resolve these oscillations and will thus need a prohibitively large number of unknowns. In our approach we use special problem dependent basis functions in the finite element method and provide an analysis for a priori and a posteriori bounds. In this way we can construct an efficient approximation method for the solution of such boundary value problems.
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