1,721,143 research outputs found
Finite Elements and Virtual Elements on Classical Meshes
No full textAmong Numerical Methods for PDEs, the Virtual Element Methods were introduced recently in order to allow the use of decompositions of the computational domain in polytopes (polygons or polyhedra) of very general shape. The present paper investigates the possible interest in their use (together or in alternative to Finite Element Methods) also for traditional decompositions (in triangles, tetrahedra, quadrilateral or hexahedra). In particular their use looks promising in problems related to high-order PDEs (requiring Cp finite dimensional spaces with p ≥ 1), as well as problems where incompressibility conditions are needed (e.g. Stokes), or problems (like mixed formulation of elasticity problems) where several useful features (symmetry of the stress tensor, possibility to hybridize, i͡nf-sup stability condition, etc.) are requested at the same time
Virtual Elements on polyhedra with a curved face
No full textWe revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper, we introduce a couple of new ideas for the construction of Virtual Element Method (VEM)-approximations on domains with curved boundary, both in two and three dimensions. The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method
Finite Dimensional Approximation of Non-Linear Problems .2. Limit Points
No full textASNUniv paris 6,f-75230 paris 05,france. ecole polytech,ctr math appl,cnrs,equipe rech 747,f-91128 palaiseau,france. univ pavia,cnr,ist anal numer,i-27100 pavia,italy. Brezzi, f, univ pavia,cnr,ist math appl,i-27100 pavia,italy.ISI Document Delivery No.: LR761Cited Reference Count: 1
Finite Dimensional Approximation of Non-Linear Problems .1. Branches of Nonsingular Solutions
No full textASNUniv paris 6,f-75230 paris 05,france. ecole polytech,ctr math appl,f-91128 palaiseau,france. univ pavia,cnr,anal numer lab,i-27100 pavia,italy. Brezzi, f, univ pavia,ist matemat appl,i-27100 pavia,italy.ISI Document Delivery No.: KU350Cited Reference Count: 1
Finite Dimensional Approximation of Non-Linear Problems .3. Simple Bifurcation Points
No full textASNUniv pavia,cnr,ist analisi numer,i-27100 pavia,italy. ecole polytech,f-91128 palaiseau,france. ecole polytech,ctr math appl,cnrs era 747,f-91128 palaiseau,france. Brezzi, f, univ pavia,ist mat appl,i-27100 pavia,italy.ISI Document Delivery No.: MN015Cited Reference Count: 2
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