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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2003 • Question 5

Question

Math 6420 • PDE Fall 2003 • Question 5

Use piecewise linear finite element basis functions with uniform grid size \(h\) and the Galerkin method to find an approximate representation for the differential equation \(a\frac {d^2u}{dx^2}+b\frac {du}{dx}+u(x)=f(x)\), with \(u(0)=0\), \(u(1)=0\), on the interval \([0,1]\). (It is only necessary to find the approximating equations, not to solve them.)

Raw LaTeX

Use piecewise linear finite element basis functions with uniform grid size \(h\) and
the Galerkin method to find an approximate representation for the differential equation
\(a\frac{d^2u}{dx^2}+b\frac{du}{dx}+u(x)=f(x)\), with \(u(0)=0\), \(u(1)=0\), on the interval
\([0,1]\). (It is only necessary to find the approximating equations, not to solve them.)

Topic Tags

Adjoint Operators and Riesz Representation Linear Programming and Optimization Orthonormal Bases and Total Sets