A convergent time-space adaptive dG(s) finite element method for parabolic problems motivated by equal error distribution
Provides a provably convergent adaptive algorithm for parabolic PDEs, addressing the need for reliable error control in numerical simulations.
Developed a fully discrete space-time adaptive method for linear parabolic problems using higher-order dG(s) finite elements, with guaranteed convergence under minimal regularity assumptions via a posteriori error indicators distributed equally in time.
We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated by the principle of equally distributing the a posteriori indicators in time and the convergence of the method is guaranteed by the uniform energy estimate from [KreuzerMöllerSchmidtSiebert:12] under minimal assumptions on the regularity of the data.