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p1afem

swMATH ID:	8489
Software Authors:	Funken, Stefan; Praetorius, Dirk; Wissgott, Philipp
Description:	Efficient implementation of adaptive P1-FEM in Matlab. We provide a Matlab package p1afem for an adaptive P1-finite element method (AFEM). This includes functions for the assembly of the data, different error estimators, and an indicator-based adaptive meshrefining algorithm. Throughout, the focus is on an efficient realization by use of Matlab built-in functions and vectorization. Numerical experiments underline the efficiency of the code which is observed to be of almost linear complexity with respect to the runtime. Although the scope of this paper is on AFEM, the general ideas can be understood as a guideline for writing efficient Matlab code
Homepage:	http://131.220.77.52/files/preprints/computational_mathematics/p1afem.pdf
Dependencies:	Matlab
Keywords:	{sc Matlab} program; finite element method; adaptivity; mesh refinement; mesh coarsening
Related Software:	Matlab; na14; iFEM; GitHub; AFEM@matlab; mfem; Gmsh; ALEA; Ameshref; FreeFem++; Octave; XFEM; T-IFISS; ALBERTA; HILBERT; DistMesh; FEniCS; deal.ii; Algorithm 949; ParaView
Cited in:	44 Publications

all top 5

all top 5

8	Computational Methods in Applied Mathematics
7	Computers & Mathematics with Applications
3	Computer Methods in Applied Mechanics and Engineering
3	Applied Mathematics and Computation
3	Journal of Scientific Computing
2	Numerical Algorithms
1	Journal of Computational Physics
1	Mathematics of Computation
1	ACM Transactions on Mathematical Software
1	BIT
1	Journal of Computational and Applied Mathematics
1	Numerische Mathematik
1	SIAM Journal on Numerical Analysis
1	Applied Numerical Mathematics
1	Computational Mechanics
1	M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
1	Linear Algebra and its Applications
1	SIAM Journal on Applied Mathematics
1	European Journal of Mechanics. A. Solids
1	Communications in Computational Physics
1	International Journal for Numerical Methods in Biomedical Engineering
1	SMAI Journal of Computational Mathematics

all top 5

41	Numerical analysis (65-XX)
14	Partial differential equations (35-XX)
8	Mechanics of deformable solids (74-XX)
3	Calculus of variations and optimal control; optimization (49-XX)
2	Approximations and expansions (41-XX)
2	Fluid mechanics (76-XX)
2	Optics, electromagnetic theory (78-XX)
2	Systems theory; control (93-XX)
1	Dynamical systems and ergodic theory (37-XX)
1	Operator theory (47-XX)
1	Probability theory and stochastic processes (60-XX)
1	Computer science (68-XX)
1	Classical thermodynamics, heat transfer (80-XX)
1	Operations research, mathematical programming (90-XX)
1	Biology and other natural sciences (92-XX)