Finite Element Interpolation
This chapter introduces the concept of finite elements along with the corresponding interpolation techniques. As an introductory example, we study how to interpolate functions in one dimension. Finite elements are then defined in arbitrary dimension, and numerous examples of scalar- and vector-valued finite elements are presented. Next, the concepts underlying the construction of meshes, approximation spaces, and interpolation operators are thoroughly investigated. The last sections of this chapter are devoted to the analysis of interpolation errors and inverse inequalities.
KeywordsInterpolation Error Approximation Space Interpolation Operator Local Degree Elemental Mass Matrix
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