Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3, Part I: countably normed spaces on polyhedral domains
From MaRDI portal
Publication:3123151
DOI10.1017/S0308210500023520zbMath0874.35019OpenAlexW2006333565MaRDI QIDQ3123151
Publication date: 10 November 1997
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0308210500023520
Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Second-order elliptic equations (35J15)
Related Items
The highest superconvergence of the tri-linear element for Schrödinger operator with singularity, Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons, ANALYTIC REGULARITY FOR LINEAR ELLIPTIC SYSTEMS IN POLYGONS AND POLYHEDRA, HIGH-ORDER GALERKIN APPROXIMATIONS FOR PARAMETRIC SECOND-ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS, Weighted analytic regularity in polyhedra, The \(hp\)-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements, Interior energy error estimates for the weak Galerkin finite element method, Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra II: Mesh Refinements and Interpolation, EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS, Exponential convergence of \(hp\)-FEM for elliptic problems in polyhedra: mixed boundary conditions and anisotropic polynomial degrees, Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type, An extension operator for Sobolev spaces with mixed weights, Exponential ReLU neural network approximation rates for point and edge singularities, Theoretical and numerical investigation of the finite cell method, Finite element analysis for the axisymmetric Laplace operator on polygonal domains, Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3. Part II: Regularity in neighbourhoods of edges, Exponential convergence of the h–p version BEM for mixed boundary value problems on polyhedrons, \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains, Boundary value problems in spaces of distributions on smooth and polygonal domains, Domain decomposition method for the \(h\)-\(p\) version finite element method, On Besov regularity of solutions to nonlinear elliptic partial differential equations, Stability and convergence of fully discrete Galerkin FEMs for the nonlinear thermistor equations in a nonconvex polygon, \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. III: Error estimates, preconditioners, computational techniques and numerical results, $hp$-dGFEM for second-order mixed elliptic problems in polyhedra, hp-FEM for three-dimensional elastic plates, Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra I:A PrioriEstimates, Exponential convergence in \(H^1\) of \textit{hp}-FEM for Gevrey regularity with isotropic singularities, \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. II: Proof of stability theorem, Stability and convergence of spectral mixed discontinuous Galerkin methods for 3D linear elasticity on anisotropic geometric meshes, Weighted Sobolev spaces and regularity for polyhedral domains, Finite element method for solving problems with singular solutions, Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D, On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains, Exponential convergence for hp-version and spectral finite element methods for elliptic problems in polyhedra, Nonlinear approximation rates and Besov regularity for elliptic PDEs on polyhedral domains, \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. I: Regularity estimates and stability theorem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The h-p version of the finite element method for problems with nonhomogeneous essential boundary condition
- Singularités en élasticité. (Singularities in elasticity)
- The h-p version of the finite element method for elliptic equations of order 2m
- Direct and inverse error estimates for finite elements with mesh refinements
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- Approximation properties of the \(h\)-\(p\) version of the finite element method
- Higher order oblique derivatives problems on polyhedral domains
- On the exponential convergence of theh-p version for boundary element Galerkin methods on polygons
- Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. II: The Trace Spaces and Application to the Boundary Value Problems with Nonhomogeneous Boundary Conditions
- Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
- The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
- Regularity and Numerical Solution of Eigenvalue Problems with Piecewise Analytic Data
- General edge asymptotics of solutions of second-order elliptic boundary value problems II
- Reliable stress and fracture mechanics analysis of complex components using a h–p version of FEM
