Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods
| Autor: | Oliver J. Sutton, Andrea Cangiani, Emmanuil H. Georgoulis |
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| Rok vydání: | 2021 |
| Předmět: |
a posteriori error estimates
Computer science Applied Mathematics Parabolic PDEs 010103 numerical & computational mathematics 01 natural sciences Mathematics::Numerical Analysis Conjunction (grammar) 010101 applied mathematics Settore MAT/08 - Analisi Numerica virtual element method Modeling and Simulation A priori and a posteriori Applied mathematics moving mesh method 0101 mathematics Element (category theory) Galerkin method |
| Zdroj: | Mathematical Models and Methods in Applied Sciences. 31:711-751 |
| ISSN: | 1793-6314 0218-2025 |
| DOI: | 10.1142/s0218202521500172 |
| Popis: | We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes which are non-hierarchical in the sense that the spatial Galerkin spaces between time-steps may be completely unrelated from one another. The practical interest of this setting is demonstrated by applying our results to finite element methods on moving meshes and using the estimators to drive an adaptive algorithm based on a virtual element method on a mesh of arbitrary polygons. The a posteriori error estimates, for the error measured in the [Formula: see text] and [Formula: see text] norms, are derived using the elliptic reconstruction technique in an abstract framework designed to precisely encapsulate our notion of inconsistency and non-hierarchicality and requiring no particular compatibility between the computational meshes used on consecutive time-steps, thereby significantly relaxing this basic assumption underlying previous estimates. |
| Databáze: | OpenAIRE |
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