2015/02/09 by Sara Pollock, Pollock, Sara
Engineering · Mathematics · #35J62 #65N12 #65N22 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1502.02629
openalex publication_date 2015/02/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
A method is developed for solving quasilinear convection diffusion problems\nstarting on a coarse mesh where the data and solution-dependent coefficients\nare unresolved, the problem is unstable and approximation properties do not\nhold. The Newton-like iterations of the solver are based on the framework of\nregularized pseudo-transient continuation where the proposed time integrator is\na variation on the Newmark strategy, designed to introduce controllable\nnumerical dissipation and to reduce the fluctuation between the iterates in the\ncoarse mesh regime where the data is rough and the linearized problems are\nbadly conditioned and possibly indefinite. An algorithm and updated marking\nstrategy is presented to produce a stable sequence of iterates as boundary and\ninternal layers in the data are captured by adaptive mesh partitioning. The\nmethod is suitable for use in an adaptive framework making use of local error\nindicators to determine mesh refinement and targeted regularization. Derivation\nand q-linear local convergence of the method is established, and numerical\nexamples demonstrate the theory including the predicted rate of convergence of\nthe iterations.\n