Finite Elements II

Alexandre Ern is Senior Researcher at Ecole des Ponts and INRIA in Paris, and he is also Associate Professor of Numerical Analysis at Ecole Polytechnique, Paris. His research deals with the devising and analysis of finite element methods and a posteriori error estimates and adaptivity with applications to fluid and solid mechanics and porous media flows. Alexandre Ern has co-authored three books and over 150 papers in peerreviewed journals. He has supervised about 20 PhD students and 10 postdoctoral fellows, and he has ongoing collaborations with several industrial partners.Jean-Luc Guermond is Professor of Mathematics at Texas A&M University where he also holds an Exxon Mobile Chair in Computational Science. His current research interests are in numerical analysis, applied mathematics, and scientific computing. He has co-authored two books and over 170 research papers in peer-reviewed journals.

• Part V: Weak formulations and well-posedness.- Weak formulation of model problems.- Main results on well-posedness.- Part VI: Galerkin approximation.- Basic error analysis.- Error analysis with variational crimes.- Linear algebra.- Sparse matrices.- Quadratures.- Part VII: Elliptic PDEs: conforming approximation.- Scalar second-order elliptic PDEs.- H1-conforming approximation (I).- H1-conforming approximation (II).- A posteriori error analysis.- The Helmholtz problem.- Part VIII: Elliptic PDEs: nonconforming approximation.- Crouzeix-Raviart approximation.- Nitsche's boundary penalty method.- Discontinuous Galerkin.- Hybrid high-order methods.- Contrasted diffusivity (I).- Contrasted diffusivity (II).- Part IX: Vector-valued elliptic PDEs.- Linear elasticity.- Maxwell's equations: H(curl)-approximation.- Maxwell's equations: control on the divergence.- Maxwell's equations: further topics.- Part X: Eigenvalue problems.- Symmetric elliptic eigenvalue problems.- Symmetric operators, conforming approximation.- Nonsymmetric problems.- Part XI: PDEs in mixed form.- Well-posedness for PDEs in mixed form.- Mixed finite element approximation.- Darcy's equations.- Potential and flux recovery.- Stokes equations: Basic ideas.- Stokes equations: Stable Pairs (I).- Stokes equations: Stable pairs (II).- Appendices.- Bijective operators in Banach spaces.