
The authors are concerned with the construction of discrete differential forms of lowest order on regular sparse grids. They analyse fairly rigorously their approximation properties and find accurate and computable approximations for nodal interpolation operators.
discrete differential forms, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, interpolation estimates, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, mixed second order problems, Numerical differentiation, hierarchical basis, Boundary value problems for second-order elliptic equations, discrete inf-sup conditions, approximate interpolation procedures, tensor product meshes, mixed finite element, multiscale decomposition
discrete differential forms, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, interpolation estimates, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, mixed second order problems, Numerical differentiation, hierarchical basis, Boundary value problems for second-order elliptic equations, discrete inf-sup conditions, approximate interpolation procedures, tensor product meshes, mixed finite element, multiscale decomposition
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