Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmi...Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.展开更多
We are concerned with a model of ionic polymer-metal composite(IPMC)materials that consists of a coupled system of the Poisson and Nernst-Planck equations,discretized by means of the finite element method(FEM).We show...We are concerned with a model of ionic polymer-metal composite(IPMC)materials that consists of a coupled system of the Poisson and Nernst-Planck equations,discretized by means of the finite element method(FEM).We show that due to the transient character of the problem it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time.We also show that due to large qualitative and quantitative differences between the two solution components,it is efficient to approximate them on different meshes using a novel adaptive multimesh hp-FEM.The study is accompanied with numerous computations and comparisons of the adaptive multimesh hp-FEMwith several other adaptive FEM algorithms.展开更多
This special issue is dedicated to the second European Seminar on Coupled Problems(ESCO 2010)that was held on June 28–July 2,2010 in Pilsen,Czech Republic.
文摘Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.
基金supported by the Grant Agency of the Academy of Sciences of the Czech Republic under Grant No.IAA100760702and by the U.S.Department of Energy Research Subcontract No.00089911+1 种基金The third author acknowledges the financial support of the U.S.Office of Naval Research under Award N000140910218The fourth author acknowledges the financial support of the Estonian Ministry of Education,grant#SF0180008s08.
文摘We are concerned with a model of ionic polymer-metal composite(IPMC)materials that consists of a coupled system of the Poisson and Nernst-Planck equations,discretized by means of the finite element method(FEM).We show that due to the transient character of the problem it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time.We also show that due to large qualitative and quantitative differences between the two solution components,it is efficient to approximate them on different meshes using a novel adaptive multimesh hp-FEM.The study is accompanied with numerous computations and comparisons of the adaptive multimesh hp-FEMwith several other adaptive FEM algorithms.
文摘This special issue is dedicated to the second European Seminar on Coupled Problems(ESCO 2010)that was held on June 28–July 2,2010 in Pilsen,Czech Republic.
