Question: 1. (4 pointsDetermine the local Lagrange shape functions on the element (0,1) for the linear and quadratic elements. 2. (1+1+2 points) Consider the BVP -u

1. (4 pointsDetermine the local Lagrange shape functions on the element

1. (4 pointsDetermine the local Lagrange shape functions on the element (0,1) for the linear and quadratic elements. 2. (1+1+2 points) Consider the BVP -u" = 2 in (0,1), u(0) = u(1) = 0. (a) Find the piecewise linear fe interpolant of the function g(x) = -2(x - 1) on the equidistant mesh consisiting of 4 elements. (b) Find the piecewise quadratic fe interpolant of the function g(x) = -2(x - 1) on the equidistant mesh consisiting of 8 elements. (c) Find the fe solution to the BVP on the equidistant mesh consisting of 4 elements using piecewise quadratic elements 1. (4 pointsDetermine the local Lagrange shape functions on the element (0,1) for the linear and quadratic elements. 2. (1+1+2 points) Consider the BVP -u" = 2 in (0,1), u(0) = u(1) = 0. (a) Find the piecewise linear fe interpolant of the function g(x) = -2(x - 1) on the equidistant mesh consisiting of 4 elements. (b) Find the piecewise quadratic fe interpolant of the function g(x) = -2(x - 1) on the equidistant mesh consisiting of 8 elements. (c) Find the fe solution to the BVP on the equidistant mesh consisting of 4 elements using piecewise quadratic elements

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