Estimating the error of a \(H^{1}\)-mixed finite element solution for the Burgers equation

Abstract

We compute error estimations for a \(H^{1}\)-mixed finite element method for Burgers equation. By using a \(H^{1}\)-mixed finite element method, the problem is reformulated as a system of first order partial differential equations, which allows an approximation of the unknown function and its derivative. Local parabolic and elliptic methods approximate the true errors from the computed solutions; the so-called a posteriori error estimates. Numerical experiments show that the error estimations converge to the true errors. References

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