A Priori and a Posteriori Error Estimates of a WOPSIP DG Method for the Heat Equation

الملخص EN

We introduce and analyze a weakly overpenalized symmetric interior penalty method for solving the heat equation.

We first provide optimal a priori error estimates in the energy norm for the fully discrete scheme with backward Euler time-stepping.

In addition, we apply elliptic reconstruction techniques to derive a posteriori error estimators, which can be used to design adaptive algorithms.

Finally, we present two numerical experiments to validate our theoretical analysis.