An Algebraic Treatment of Essential Boundary Conditions in the Particle–Partition of Unity Method

DOI10.1137/080716499zbMath1189.65284OpenAlexW1981494985MaRDI QIDQ3558705

Marc Alexander Schweitzer

Publication date: 6 May 2010

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080716499

zbMATH Keywords

complexitynumerical resultsPoisson equationpartition of unity methodNitsche's methodmeshfree methodsecond order elliptic equationessential boundary conditionsglobal splitting

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (9)

Generalizations of the finite element method ⋮ A partition of unity method with penalty for fourth order problems ⋮ Treatment of general domains in two space dimensions in a Partition of Unity Method ⋮ Orbital-enriched flat-top partition of unity method for the Schrödinger eigenproblem ⋮ Stable enrichment and local preconditioning in the particle-partition of unity method ⋮ Multilevel particle-partition of unity method ⋮ Dispersion Properties of the Partition of Unity Method and Explicit Dynamics ⋮ Multilevel Partition of Unity Method for Elliptic Problems with Strongly Discontinuous Coefficients ⋮ Exact imposition of essential boundary condition and material interface continuity in Galerkin‐based meshless methods

Uses Software

• XFEM

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