ENO schemes with subcell resolution
Journal of Computational Physics
Adaptive refinement of unstructured finite-element meshes
Finite Elements in Analysis and Design
A new and simple algorithm for quality 2-dimensional mesh generation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Adaptive Methods for Partial Differential Equations
Adaptive Methods for Partial Differential Equations
A Parallel Algorithm for the Dynamic Partitioning of Particle-Mesh Computational Systems
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Index translation schemes for adaptive computations on distributed memory multicomputers
IPPS '95 Proceedings of the 9th International Symposium on Parallel Processing
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Particle tracking methods are a versatile computational technique central to the simulation of a wide range of scientific applications. In this paper we present an a posteriori error estimator for adaptive mesh refinement (AMR) using particle tracking methods. The approach uses a parallel computing framework, the "in-element" particle tracking method, based on the assumption that particle trajectories are computed by problem data localized to individual elements. Adaptive mesh refinement is used to control the mesh discretization errors along computed characteristics of the particle trajectories. Traditional a posteriori error estimators for AMR methods inherit flaws from the discrete solution of time-marching partial differential equations (PDEs)--particularly for advection/convection-dominated transport applications. To address this problem we introduce a new a posteriori error estimator based on particle tracking methods. We present experimental results that detail the performance of a parallel implementation of this particle method approach for a two-dimensional, time-marching convection-diffusion benchmark problem on an unstructured, adaptive mesh.