MooAFEM: an object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs

DOI10.1016/j.amc.2022.127731OpenAlexW4312057265MaRDI QIDQ2700349

Michael Innerberger, Dirk Praetorius

Publication date: 21 April 2023

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.01845

zbMATH Keywords

adaptivityfinite element softwareiterative linearizationhigher-order FEMobject oriented design

Mathematics Subject Classification ID

Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) (68N19) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Software, source code, etc. for problems pertaining to partial differential equations (35-04)

Related Items (4)

Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs ⋮ Plain convergence of goal-oriented adaptive FEM ⋮ MATLAB implementation of hp finite elements on rectangles using hierarchical basis functions ⋮ MooAFEM

Uses Software

• Matlab
• DUNE
• deal.ii
• FEniCS
• iFEM
• NGSolve
• GitHub
• oFEM
• varfem

Cites Work

• Axioms of adaptivity
• On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection
• Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis
• Theory and practice of finite elements.
• Efficient and flexible Matlab implementation of 2D and 3D elastoplastic problems
• Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
• Fast Matlab evaluation of nonlinear energies using FEM in 2D and 3D: nodal elements
• The \textsc{Dune} framework: basic concepts and recent developments
• The \textsc{deal.II} finite element library: design, features, and insights
• Instance-optimal goal-oriented adaptivity
• Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data
• \(o\) FEM: an object oriented finite element package for Matlab
• Efficient implementation of adaptive P1-FEM in Matlab
• Optimality of a standard adaptive finite element method
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• An Abstract Analysis of Optimal Goal-Oriented Adaptivity
• Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
• A Goal-Oriented Adaptive Finite Element Method with Convergence Rates
• Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex
• The Finite Element Method with Penalty
• A Convergent Adaptive Algorithm for Poisson’s Equation
• The completion of locally refined simplicial partitions created by bisection
• Finite Difference Approximation for Pricing the American Lookback Option
• Instance optimality of the adaptive maximum strategy
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