Error estimates for shock capturing finite element approximations of the one dimensional Burgers' equation
This work offers theoretical error bounds for shock capturing finite element methods, relevant for numerical analysts working on hyperbolic conservation laws.
The paper provides error estimates in weak norms for a shock capturing finite element method applied to the 1D Burgers' equation, with robustness in the inviscid limit. Using a total variation bound and interpolation, error estimates in L^p-norms are derived.
We propose an error analysis in weak norms of a shock capturing finite element method for the Burgers' equation. The estimates can be related to estimates of certain filtered quantities and are robust in the inviscid limit. Using a total variation apriori bound on the discrete solution and an interpolation inequality error estimates in $L^p$-norms can are obtained using interpolation.