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Exercise 10: Estimates of accuracy.     continued...

The topic of providing accuracy estimates of numerical solutions and providing algorithms to automatically increase the accuracy of a solution has (and continues to be) of considerable interest and research. This type of research can be found under the heading adaptive methods for partial differential equations, and in many books on finite element methods. Before reading the brief introduction to adaptive methods given below, try to figure out how to estimate the accuracy of your numerical solution and give some thought to how you could increase the accuracy of the solution.