A posteriori error estimates of hphp-discontinuous Galerkin method for strongly nonlinear elliptic problems

In this paper, we study the residual-based a posteriori error estimates of hphp-discontinuous Galerkin finite element methods for strongly nonlinear elliptic boundary value problems. Computable upper and lower bounds on the error are derived in a natural mesh-dependent energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. Numerical experiments are also provided to illustrate the performance of the proposed estimators.