Adaptive discontinuous Galerkin approximations to fourth order parabolic problems
For researchers solving fourth-order parabolic PDEs, this work provides an adaptive method that improves efficiency, though it is an incremental extension of existing techniques.
The paper develops an adaptive algorithm for fourth-order parabolic problems using residual-based a posteriori error indicators, achieving substantial reduction in computational effort.
An adaptive algorithm, based on residual type a posteriori indicators of errors measured in $L^{\infty}(L^2)$ and $L^2(L^2)$ norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local spatial polynomial degrees $r\ge 2$. The a posteriori estimates are then used within an adaptive algorithm, highlighting their relevance in practical computations, which results into substantial reduction of computational effort.