Finite Elements II: Galerkin Approximation, Elliptic and Mixed Pdes (Hardcover, 2021)

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.