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FEM:010117Two P1 elements for -u''+u=1 with Robin: free A [[13/3,-23/12],[-23/12,25/6]], u=(0,63/109,114/109), reaction -148/109

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Fem Robin Reaction Diffusion AssemblyFem Constrained Row Discrete Reaction

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Mixed review

FEM:010118One-mode Ritz for -u''=x: a=1/4, uh=x(1-x)/4, min J=-1/96, energy-error squared 1/720

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Fem One Mode Ritz PoissonFem Energy Error Galerkin Orthogonality

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Mixed review

FEM:010119Symmetric Nitsche on one P1 interval: stiffness 3, load 6, uh=2(1-x), coercive here iff gamma>1

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Fem Symmetric Nitsche DirichletFem Nitsche One Mode Coercivity

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Mixed review

FEM:010220P1 triangle (0,0),(2,0),(0,1) with k=3,q=6: K=[[15/4,-3/4,-3],[-3/4,3/4,0],[-3,0,3]], energy 39

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Fem P1 Triangle StiffnessFem Affine Gradient Energy

Reference elements, interpolation, and numerical quadratureFinite Element Methods · Mixed review

FEM:010221Quadratic [0,1] Gauss: K exact at 2 pts, M2 singular on (2,-1,2), exact v^T M v=4/5

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Fem Quadratic Gauss QuadratureFem Mass Matrix Exactness

Reference elements, interpolation, and numerical quadratureFinite Element Methods · Mixed review

FEM:010222Cubic Hermite cantilever L=2, EI=6, q=12 has tip (4,8/3), support residual (-24,-24), midpoint 4/3 not 17/12

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Fem Cubic Hermite InterpolationFem Consistent Beam Loading

Reference elements, interpolation, and numerical quadratureFinite Element Methods · Mixed review

FEM:010323Two CCW triangles on the unit square give K with free u2=u4=1/2 and reactions r1=-1/2, r3=1/2

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Fem P1 Triangle StiffnessFem Global Scatter Reaction

Global assembly and essential or natural boundary conditionsFinite Element Methods · Mixed review

FEM:010324MPC u3=u1+u2 with K=diag(2,3,4) reduces to q=(7/13,9/13) and lambda=-12/13

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Fem Multipoint TransformationFem Kkt Multiplier Recovery

Global assembly and essential or natural boundary conditionsFinite Element Methods · Mixed review

FEM:010325Condensing internal dof 3 from the given 3x3 yields boundary (7/5,57/35) and internal 52/35

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Fem Static CondensationFem Interior Dof Recovery

Global assembly and essential or natural boundary conditionsFinite Element Methods · Mixed review

FEM:010426Qh=11/4,35/16,131/64 on h=1/2,1/4,1/8 has ratio 4, observed p=2, Richardson value 2, and C=3

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Fem Observed Convergence OrderFem Richardson Extrapolation

Stability, consistency, a priori error, and adaptivityFinite Element Methods · Mixed review

FEM:010427Dorfler theta=0.70 on squared indicators (16,4,1,1) marks only {K1} with share 8/11

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Fem Dorfler Bulk MarkingFem Squared Indicator Threshold

Stability, consistency, a priori error, and adaptivityFinite Element Methods · Mixed review

FEM:010528Linearized buckling K phi = P G phi has Pcr=3-sqrt(3) and G-normalized low mode

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Fem Linearized Buckling EigenvalueFem Geometric Stiffness Generalized Eigen

Time-dependent and eigenvalue finite-element systemsFinite Element Methods · Mixed review

FEM:010529One Newmark average-acceleration step on m=2,k=8 is u1=3/5 with energy 4

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Fem Newmark Average AccelerationFem Undamped Sdof Discrete Energy

Time-dependent and eigenvalue finite-element systemsFinite Element Methods · Mixed review

FEM:010630Two consistent-tangent Newton steps from u0=1/2 give u2=536/511, not the root 1

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Fem Consistent Tangent NewtonFem Residual Jacobian Recompute

Nonlinear, constrained, and mixed formulationsFinite Element Methods · Mixed review

FEM:010631Active-set contact on K[[2,-1],[-1,2]] is u=(0,3/2), lambda=(1/2,0), energy -9/4

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Fem Unilateral Contact Active SetFem Kkt Complementarity Contact

Nonlinear, constrained, and mixed formulationsFinite Element Methods · Mixed review