A Hybrid Analytical-Numerical Technique for Elliptic PDEs
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Publication:4632008
DOI10.1137/18M1217309zbMath1414.65039WikidataQ114074285 ScholiaQ114074285MaRDI QIDQ4632008
Matthew J. Colbrook, Parham Hashemzadeh, Thanasis S. Fokas
Publication date: 25 April 2019
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)
Related Items (6)
Linear evolution equations on the half-line with dynamic boundary conditions ⋮ The Fokas method for the Broer-Kaup system on the half-line ⋮ The Unified Transform and the Water Wave Problem ⋮ The unified transform for mixed boundary condition problems in unbounded domains ⋮ A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics ⋮ Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters
Uses Software
Cites Work
- Numerical analysis of Fokas' unified method for linear elliptic PDEs
- Fokas integral equations for three dimensional layered-media scattering
- Stability of periodic gravity waves in the presence of surface tension
- Elliptic PDEs with constant coefficients on convex polyhedra via the unified method
- An analytical method for linear elliptic PDEs and its numerical implementation
- A fast and simple algorithm for the computation of Legendre coefficients
- Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains
- Fourier-Mellin transforms for circular domains
- The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
- A semi-analytical numerical method for solving evolution and elliptic partial differential equations
- Direct and iterative solution of the generalized Dirichlet-Neumann map for elliptic PDEs on square domains
- Singularities and treatments of elliptic boundary value problems.
- Spectral element methods for elliptic problems in nonsmooth domains
- Optimal estimates for lower and upper bounds of approximation errors in the \(p\)-version of the finite element method in two dimensions
- On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains
- Auswertung der Normen von Interpolationsoperatoren
- On the integrability of linear and nonlinear partial differential equations
- A transform method for Laplace's equation in multiply connected circular domains
- Evaluation of Layer Potentials Close to the Boundary for Laplace and Helmholtz Problems on Analytic Planar Domains
- The solution of linear constant-coefficient evolution PDEs with periodic boundary conditions
- The instability of periodic surface gravity waves
- A non-local formulation of rotational water waves
- Recovering the Water-Wave Profile from Pressure Measurements
- Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
- The Unified Transform for the modified Helmholtz equation in the exterior of a square
- A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon
- A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain
- A Fast Algorithm for the Evaluation of Legendre Expansions
- A new transform method I: domain-dependent fundamental solutions and integral representations
- Approximation Results for Orthogonal Polynomials in Sobolev Spaces
- Fast algorithms for discrete polynomial transforms
- Construction of Corner Singularities for Agmon-Douglis-Nirenberg Elliptic Systems
- A unified transform method for solving linear and certain nonlinear PDEs
- The numerical stability of barycentric Lagrange interpolation
- A transform method for the biharmonic equation in multiply connected circular domains
- The unified transform for mixed boundary condition problems in unbounded domains
- Advances in the study of boundary value problems for nonlinear integrable PDEs
- Stokes flow through a two-dimensional channel with a linear expansion
- Interface Problems for Dispersive Equations
- Elliptic equations with low regularity boundary data via the unified method
- Reviving the Method of Particular Solutions
- On the rigorous foundations of the Fokas method for linear elliptic partial differential equations
- Solving Wiener–Hopf problems without kernel factorization
- A numerical technique for linear elliptic partial differential equations in polygonal domains
- On the convergence rates of Legendre approximation
- The inverse water wave problem of bathymetry detection
- The Method of Fokas for Solving Linear Partial Differential Equations
- A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs
- On a new non-local formulation of water waves
- The p‐version of the finite element method for domains with corners and for infinite domains
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