Update ellip test to solve p-Bratu instead of plain p-Laplacian.

Make ellip tests use -snes_monitor_short.
jedbrown · Sep 17, 2009 · 878c4fd · 878c4fd
1 parent a52d383
commit 878c4fd
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diff --git a/src/fs/tests/CMakeLists.txt b/src/fs/tests/CMakeLists.txt
@@ -11,8 +11,9 @@ dohp_add_test (fs-mf-op-proj-1  1 fs-ex1 -const_BDeg 7 -snes_mf_operator -ksp_co
 
 dohp_add_test (bu-0 1 bu -dmesh_in "${Dohp_DATA_DIR}/dblock211.h5m" -dfs_ordering_type natural)
 
-dohp_add_test (ellip-e0-b2-p18 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor -ksp_monitor -pc_type lu -exact_a 1.6 -exact_b 1.7 -exact_c 1.8 -exact 0 -const_bdeg 2 -ellip_p 1.6 -dfs_ordering_type natural)
-dohp_add_test (ellip-e0-b4-p18 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor -ksp_monitor -pc_type lu -exact_a 1.6 -exact_b 1.7 -exact_c 1.8 -exact 0 -const_bdeg 4 -ellip_p 1.6 -djac_tensor_no_unroll -dfs_ordering_type natural)
-dohp_add_test (ellip-e0-b4-p17-sse 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor -ksp_monitor -pc_type lu -exact_a 1.6 -exact_b 1.7 -exact_c 1.8 -exact 0 -const_bdeg 4 -ellip_p 1.4 -dfs_ordering_type natural)
+dohp_add_test (ellip-e0-b2-p16 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor_short -ksp_monitor_short -pc_type lu -exact_a 1.6 -exact_b 1.7 -exact_c 1.8 -exact 0 -const_bdeg 2 -ellip_p 1.6 -dfs_ordering_type natural)
+dohp_add_test (ellip-e0-b4-p16 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor_short -ksp_monitor_short -pc_type lu -exact_a 1.6 -exact_b 1.7 -exact_c 1.8 -exact 0 -const_bdeg 4 -ellip_p 1.6 -djac_tensor_no_unroll -dfs_ordering_type natural)
+dohp_add_test (ellip-e0-b4-p14-sse 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor_short -ksp_monitor_short -pc_type lu -exact_a 1.6 -exact_b 1.7 -exact_c 1.8 -exact 0 -const_bdeg 4 -ellip_p 1.4)
+dohp_add_test (ellip-e0-b4-p17-lam1-sse 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor_short -ksp_monitor_short -pc_type lu -exact 0 -const_bdeg 4 -ellip_p 1.7 -ellip_lam 1)
 dohp_add_test (ellip-morph 1 ellip -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -morph 1 -twist 0.4 -ksp_monitor_short -snes_max_it 1 -ksp_rtol 1e-8 -ksp_type cg -pc_type lu)
 dohp_add_test (elast-e0-b4-g01 1 elast -dmesh_in "${Dohp_DATA_DIR}/dblock4.h5m" -snes_monitor_short -ksp_monitor_short -pc_type ilu -exact_a 0.98 -exact_b 1.01 -exact_c 1.01 -exact 0 -const_bdeg 4 -elast_gamma 0.1)
diff --git a/src/fs/tests/ellip.c b/src/fs/tests/ellip.c
@@ -1,6 +1,6 @@
-static const char help[] = "Solve a scalar elliptic problem, a regularized p-Laplacian using dual order hp elements.\n"
+static const char help[] = "Solve a scalar elliptic problem, a regularized p-Bratu using dual order hp elements.\n"
   "The model problem is\n"
-  "  \\int_\\Omega (\\eta Dv \\cdot Du - f v) - \\int_\\Gamma v (\\eta Du \\cdot n) = 0\n"
+  "  \\int_\\Omega (\\eta Dv \\cdot Du - \\lambda e^u - f v) - \\int_\\Gamma v (\\eta Du \\cdot n) = 0\n"
   "where\n"
   "  \\eta(u) = (\\epsilon + 1/2 Du . Du)^(p-2)\n"
   "  (\\eta Du \\cdot n) = known OR function of u OR self (\"No condition\" outflow)\n\n";
@@ -23,6 +23,7 @@ typedef struct {
 struct EllipParam {
   dReal epsilon;
   dReal p;
+  dReal lambda;
   dTruth onlyproject;
   dTruth bdy100;
 };
@@ -99,8 +100,9 @@ static void EllipExact_3_Forcing(const struct EllipExactCtx *ctx,const struct El
 }
 
 struct EllipStore {
-  dReal eta,deta;
-  dReal Du[3];
+  dReal eta;
+  dReal sqrt_mdeta_Du[3];
+  dReal lambda_exp_u;
 };
 
 struct EllipCtx {
@@ -136,6 +138,7 @@ static dErr EllipCreate(MPI_Comm comm,Ellip *ellip)
   prm = &elp->param;
   prm->p           = 2.0;       /* p in p-Laplacian */
   prm->epsilon     = 1.0;
+  prm->lambda      = 0.0;       /* Bratu nonlinearity */
   prm->onlyproject = dFALSE;
 
   *ellip = elp;
@@ -175,6 +178,7 @@ static dErr EllipSetFromOptions(Ellip elp)
     err = PetscOptionsTruth("-eta_monitor","Monitor nonlinearity","",elp->eta_monitor,&elp->eta_monitor,NULL);dCHK(err);
     err = PetscOptionsReal("-ellip_p","p in p-Laplacian","",prm->p,&prm->p,NULL);dCHK(err);
     err = PetscOptionsReal("-ellip_eps","Regularization in p-Laplacian","",prm->epsilon,&prm->epsilon,NULL);dCHK(err);
+    err = PetscOptionsReal("-ellip_lam","Strength of Bratu nonlinearity","",prm->lambda,&prm->lambda,NULL);dCHK(err);
     err = PetscOptionsTruth("-onlyproject","Actually just do a projection","",prm->onlyproject,&prm->onlyproject,NULL);dCHK(err);
     err = PetscOptionsTruth("-bdy100","Only use boundary 100","",prm->bdy100,&prm->bdy100,NULL);dCHK(err);
     err = PetscOptionsInt("-exact","Exact solution choice","",exact,&exact,NULL);dCHK(err);
@@ -285,12 +289,13 @@ static dErr EllipDestroy(Ellip elp)
 
 static inline void EllipPointwiseComputeStore(struct EllipParam *prm,const dReal dUNUSED x[3],const dScalar dUNUSED u[1],const dScalar Du[3],struct EllipStore *st)
 {
-  dReal gamma,espg,p=prm->p;
+  dReal gamma,espg,p=prm->p,sqrt_mdeta;
   gamma = 0.5 * (dSqr(Du[0]) + dSqr(Du[1]) + dSqr(Du[2]));
   espg = dSqr(prm->epsilon) + gamma;
   st->eta = pow(espg,(p-2)/2);
-  st->deta = ((p-2)/2) * st->eta / espg;
-  st->Du[0] = Du[0]; st->Du[1] = Du[1]; st->Du[2] = Du[2];
+  sqrt_mdeta = sqrt(-((p-2)/2) * st->eta / espg);
+  for (dInt i=0; i<3; i++) st->sqrt_mdeta_Du[i] = sqrt_mdeta*Du[i];
+  st->lambda_exp_u = prm->lambda * exp(u[0]);
 }
 
 static inline void EllipPointwiseFunction(struct EllipParam *prm,struct EllipExact *exact,struct EllipExactCtx *exactctx,
@@ -305,26 +310,25 @@ static inline void EllipPointwiseFunction(struct EllipParam *prm,struct EllipExa
     v[0] += weight * u[0];
     Dv[0] = Dv[1] = Dv[2] = 0;
   } else {
+    v[0] += -weight * st->lambda_exp_u;
     for (dInt i=0; i<3; i++) {
       Dv[i] = weight * st->eta * Du[i]; /* Coefficient of Dv in weak form */
-  }
+    }
   }
 }
 
 static inline void EllipPointwiseJacobian(struct EllipParam dUNUSED *prm,const struct EllipStore *restrict st,dReal weight,
-                                          const dScalar dUNUSED u[restrict static 1],const dScalar Du[restrict static 3],
+                                          const dScalar u[restrict static 1],const dScalar Du[restrict static 3],
                                           dScalar v[restrict static 1],dScalar Dv[restrict static 3])
 {
-  const dScalar dot = dDotScalar3(st->Du,Du);
-  const dReal etaw = st->eta*weight,dotdetaw = dot*st->deta*weight;
+  const dScalar dotw = dDotScalar3(st->sqrt_mdeta_Du,Du)*weight;
+  const dReal etaw = st->eta*weight;
   if (prm->onlyproject) {
     v[0] = weight * u[0];
     Dv[0] = Dv[1] = Dv[2] = 0;
   } else {
-    v[0] = 0;
-    Dv[0] = etaw*Du[0] + dotdetaw*st->Du[0];
-    Dv[1] = etaw*Du[1] + dotdetaw*st->Du[1];
-    Dv[2] = etaw*Du[2] + dotdetaw*st->Du[2];
+    v[0] = -weight * st->lambda_exp_u * u[0];
+    for (dInt i=0; i<3; i++) Dv[i] = etaw*Du[i] - dotw*st->sqrt_mdeta_Du[i];
   }
 }
 
@@ -363,20 +367,6 @@ static dErr EllipFunction(SNES dUNUSED snes,Vec gx,Vec gy,void *ctx)
   }
   err = dFSRestoreWorkspace(fs,__func__,&q,&jinv,&jw,&u,&v,&du,&dv);dCHK(err);
   err = dFSRestoreElements(fs,&n,&off,&rule,&efs,&geomoff,&geom);dCHK(err);
-#if 0
-  if (0) {
-    dMeshESH *sets;
-    dInt nsets;
-    err = dFSGetBoundarySets(fs,100,&nsets,&sets);dCHK(err);
-    for (dInt s=0; s<nsets; s++) {
-      err = dFSGetElements(fs,sets[s],&n,&off,&rule,&efs,&geomoff,&geom);dCHK(err);
-      for (dInt e=0; e<n; e++) {
-        // integrate weak forms over faces
-      }
-      err = dFSRestoreElements(fs,sets[s],&n,&off,&rule,&efs,&geomoff,&geom);dCHK(err);
-    }
-  }
-#endif
   err = VecRestoreArray(elp->x,&x);dCHK(err);
   err = VecRestoreArray(elp->y,&y);dCHK(err);
   err = dFSExpandedToGlobal(fs,elp->y,gy,dFS_INHOMOGENEOUS,INSERT_VALUES);dCHK(err);
@@ -518,12 +508,12 @@ static dErr EllipJacobian(SNES dUNUSED snes,Vec gx,Mat *J,Mat *Jp,MatStructure *
                 dReal v[1],Dv[3];
                 EllipPointwiseJacobian(&elp->param,&st,jw[lq],u,Du,v,Dv);
 #  if Q1SCALE
-                K[ltest][lp] += //basis[lq][ltest] * v[0]
+                K[ltest][lp] += basis[lq][ltest] * v[0] +
                   lscale[ltest]*lscale[lp]*(+ deriv[lq][ltest][0] * Dv[0]
                                             + deriv[lq][ltest][1] * Dv[1]
                                             + deriv[lq][ltest][2] * Dv[2]);
 #  else
-                K[ltest][lp] += //basis[lq][ltest] * v[0]
+                K[ltest][lp] += basis[lq][ltest] * v[0] +
                   (+ deriv[lq][ltest][0] * Dv[0]
                    + deriv[lq][ltest][1] * Dv[1]
                    + deriv[lq][ltest][2] * Dv[2]);

diff --git a/src/fs/tests/refout/ellip-e0-b2-p16.refout b/src/fs/tests/refout/ellip-e0-b2-p16.refout
@@ -0,0 +1,17 @@
+  0 SNES Function norm 3.17818 
+    0 KSP Residual norm 3.75851 
+    1 KSP Residual norm < 1.e-11
+  1 SNES Function norm 0.152157 
+    0 KSP Residual norm 0.199466 
+    1 KSP Residual norm < 1.e-11
+  2 SNES Function norm 0.000928224 
+    0 KSP Residual norm 0.00116026 
+    1 KSP Residual norm < 1.e-11
+  3 SNES Function norm 4.24861e-08 
+    0 KSP Residual norm 5.05985e-08 
+    1 KSP Residual norm < 1.e-11
+  4 SNES Function norm < 1.e-11
+Algebraic residual        |x|_1 9.35e-16  |x|_2 2.59e-16  |x|_inf 1.67e-16
+Interpolation residual    |x|_1 2.43e-01  |x|_2 6.74e-02  |x|_inf 3.37e-02
+Pointwise solution error  |x|_1 3.80e-01  |x|_2 2.13e-01  |x|_inf 3.03e-01
+Pointwise gradient error  |x|_1 8.22e+00  |x|_2 7.19e+00  |x|_inf 1.59e+01
diff --git a/src/fs/tests/refout/ellip-e0-b2-p18.refout b/src/fs/tests/refout/ellip-e0-b2-p18.refout
diff --git a/src/fs/tests/refout/ellip-e0-b4-p14-sse.refout b/src/fs/tests/refout/ellip-e0-b4-p14-sse.refout
@@ -0,0 +1,109 @@
+  0 SNES Function norm 3.08243 
+    0 KSP Residual norm 49.3455 
+    1 KSP Residual norm 7.44349 
+    2 KSP Residual norm 3.97315 
+    3 KSP Residual norm 2.15976 
+    4 KSP Residual norm 1.20451 
+    5 KSP Residual norm 0.698012 
+    6 KSP Residual norm 0.39404 
+    7 KSP Residual norm 0.183079 
+    8 KSP Residual norm 0.098371 
+    9 KSP Residual norm 0.0557577 
+   10 KSP Residual norm 0.0296621 
+   11 KSP Residual norm 0.0162693 
+   12 KSP Residual norm 0.00891964 
+   13 KSP Residual norm 0.00537996 
+   14 KSP Residual norm 0.00337431 
+   15 KSP Residual norm 0.00210799 
+   16 KSP Residual norm 0.00127631 
+   17 KSP Residual norm 0.000769679 
+   18 KSP Residual norm 0.000454002 
+  1 SNES Function norm 2.36119 
+    0 KSP Residual norm 42.3983 
+    1 KSP Residual norm 13.982 
+    2 KSP Residual norm 5.18871 
+    3 KSP Residual norm 2.46515 
+    4 KSP Residual norm 0.96147 
+    5 KSP Residual norm 0.386276 
+    6 KSP Residual norm 0.129491 
+    7 KSP Residual norm 0.0630208 
+    8 KSP Residual norm 0.0244245 
+    9 KSP Residual norm 0.0103638 
+   10 KSP Residual norm 0.00498037 
+   11 KSP Residual norm 0.00255219 
+   12 KSP Residual norm 0.00107896 
+   13 KSP Residual norm 0.00052551 
+   14 KSP Residual norm 0.000263445 
+  2 SNES Function norm 0.57823 
+    0 KSP Residual norm 4.07038 
+    1 KSP Residual norm 1.79894 
+    2 KSP Residual norm 0.744108 
+    3 KSP Residual norm 0.310638 
+    4 KSP Residual norm 0.129062 
+    5 KSP Residual norm 0.0560168 
+    6 KSP Residual norm 0.0283736 
+    7 KSP Residual norm 0.0140375 
+    8 KSP Residual norm 0.00759276 
+    9 KSP Residual norm 0.0034378 
+   10 KSP Residual norm 0.00116475 
+   11 KSP Residual norm 0.000500336 
+   12 KSP Residual norm 0.000237274 
+   13 KSP Residual norm 0.000110793 
+   14 KSP Residual norm 5.4996e-05 
+   15 KSP Residual norm 2.93445e-05 
+  3 SNES Function norm 0.0557488 
+    0 KSP Residual norm 0.268575 
+    1 KSP Residual norm 0.115653 
+    2 KSP Residual norm 0.0447676 
+    3 KSP Residual norm 0.0202612 
+    4 KSP Residual norm 0.00819633 
+    5 KSP Residual norm 0.00343241 
+    6 KSP Residual norm 0.00155376 
+    7 KSP Residual norm 0.000784417 
+    8 KSP Residual norm 0.000423942 
+    9 KSP Residual norm 0.00021626 
+   10 KSP Residual norm 6.97143e-05 
+   11 KSP Residual norm 3.04921e-05 
+   12 KSP Residual norm 1.24375e-05 
+   13 KSP Residual norm 5.88531e-06 
+   14 KSP Residual norm 3.1101e-06 
+   15 KSP Residual norm 1.65415e-06 
+  4 SNES Function norm 0.000346418 
+    0 KSP Residual norm 0.00186954 
+    1 KSP Residual norm 0.000836923 
+    2 KSP Residual norm 0.000322917 
+    3 KSP Residual norm 0.000140581 
+    4 KSP Residual norm 5.06626e-05 
+    5 KSP Residual norm 1.9646e-05 
+    6 KSP Residual norm 8.13219e-06 
+    7 KSP Residual norm 4.27875e-06 
+    8 KSP Residual norm 2.17908e-06 
+    9 KSP Residual norm 1.13513e-06 
+   10 KSP Residual norm 4.3265e-07 
+   11 KSP Residual norm 2.06638e-07 
+   12 KSP Residual norm 8.7329e-08 
+   13 KSP Residual norm 3.74862e-08 
+   14 KSP Residual norm 1.75962e-08 
+  5 SNES Function norm 2.60663e-08 
+    0 KSP Residual norm 1.37492e-07 
+    1 KSP Residual norm 6.25593e-08 
+    2 KSP Residual norm 2.55046e-08 
+    3 KSP Residual norm 1.19925e-08 
+    4 KSP Residual norm 4.81454e-09 
+    5 KSP Residual norm 2.4683e-09 
+    6 KSP Residual norm 1.37205e-09 
+    7 KSP Residual norm 7.914e-10 
+    8 KSP Residual norm 3.593e-10 
+    9 KSP Residual norm 1.500e-10 
+   10 KSP Residual norm 5.967e-11 
+   11 KSP Residual norm 3.153e-11 
+   12 KSP Residual norm 1.643e-11 
+   13 KSP Residual norm < 1.e-11
+   14 KSP Residual norm < 1.e-11
+   15 KSP Residual norm < 1.e-11
+   16 KSP Residual norm < 1.e-11
+  6 SNES Function norm < 1.e-11
+Algebraic residual        |x|_1 4.85e-12  |x|_2 1.95e-13  |x|_inf 4.73e-14
+Interpolation residual    |x|_1 4.90e-02  |x|_2 2.56e-03  |x|_inf 4.11e-04
+Pointwise solution error  |x|_1 1.14e-03  |x|_2 7.55e-04  |x|_inf 2.68e-03
+Pointwise gradient error  |x|_1 4.85e+00  |x|_2 5.11e+00  |x|_inf 1.70e+01
diff --git a/src/fs/tests/refout/ellip-e0-b4-p16.refout b/src/fs/tests/refout/ellip-e0-b4-p16.refout
@@ -0,0 +1,106 @@
+  0 SNES Function norm 4.93408 
+    0 KSP Residual norm 51.7059 
+    1 KSP Residual norm 6.79209 
+    2 KSP Residual norm 2.7863 
+    3 KSP Residual norm 1.50687 
+    4 KSP Residual norm 0.747774 
+    5 KSP Residual norm 0.374842 
+    6 KSP Residual norm 0.174141 
+    7 KSP Residual norm 0.0784086 
+    8 KSP Residual norm 0.0389488 
+    9 KSP Residual norm 0.0193889 
+   10 KSP Residual norm 0.0100507 
+   11 KSP Residual norm 0.00610852 
+   12 KSP Residual norm 0.00343091 
+   13 KSP Residual norm 0.00190266 
+   14 KSP Residual norm 0.00102771 
+   15 KSP Residual norm 0.000539639 
+   16 KSP Residual norm 0.000292823 
+  1 SNES Function norm 2.62495 
+    0 KSP Residual norm 16.3713 
+    1 KSP Residual norm 6.34626 
+    2 KSP Residual norm 2.33583 
+    3 KSP Residual norm 0.998847 
+    4 KSP Residual norm 0.392279 
+    5 KSP Residual norm 0.157428 
+    6 KSP Residual norm 0.0496749 
+    7 KSP Residual norm 0.0206766 
+    8 KSP Residual norm 0.0114255 
+    9 KSP Residual norm 0.00679726 
+   10 KSP Residual norm 0.00294285 
+   11 KSP Residual norm 0.0012573 
+   12 KSP Residual norm 0.000521005 
+   13 KSP Residual norm 0.000213325 
+   14 KSP Residual norm 9.09341e-05 
+  2 SNES Function norm 1.08788 
+    0 KSP Residual norm 5.39009 
+    1 KSP Residual norm 1.80249 
+    2 KSP Residual norm 0.628344 
+    3 KSP Residual norm 0.265499 
+    4 KSP Residual norm 0.100997 
+    5 KSP Residual norm 0.0357152 
+    6 KSP Residual norm 0.0124749 
+    7 KSP Residual norm 0.0047978 
+    8 KSP Residual norm 0.0022914 
+    9 KSP Residual norm 0.00125394 
+   10 KSP Residual norm 0.000622427 
+   11 KSP Residual norm 0.000285466 
+   12 KSP Residual norm 0.000142561 
+   13 KSP Residual norm 6.54096e-05 
+   14 KSP Residual norm 2.795e-05 
+  3 SNES Function norm 0.0756234 
+    0 KSP Residual norm 0.461806 
+    1 KSP Residual norm 0.225487 
+    2 KSP Residual norm 0.0890375 
+    3 KSP Residual norm 0.0359211 
+    4 KSP Residual norm 0.0121965 
+    5 KSP Residual norm 0.00429802 
+    6 KSP Residual norm 0.00196438 
+    7 KSP Residual norm 0.00102016 
+    8 KSP Residual norm 0.000570907 
+    9 KSP Residual norm 0.000282919 
+   10 KSP Residual norm 8.64812e-05 
+   11 KSP Residual norm 4.16991e-05 
+   12 KSP Residual norm 2.14124e-05 
+   13 KSP Residual norm 1.0569e-05 
+   14 KSP Residual norm 5.43069e-06 
+   15 KSP Residual norm 2.91421e-06 
+  4 SNES Function norm 0.000462468 
+    0 KSP Residual norm 0.00247013 
+    1 KSP Residual norm 0.00124566 
+    2 KSP Residual norm 0.000471243 
+    3 KSP Residual norm 0.000174178 
+    4 KSP Residual norm 6.61506e-05 
+    5 KSP Residual norm 2.40872e-05 
+    6 KSP Residual norm 1.01713e-05 
+    7 KSP Residual norm 4.01465e-06 
+    8 KSP Residual norm 1.86325e-06 
+    9 KSP Residual norm 1.03734e-06 
+   10 KSP Residual norm 5.39176e-07 
+   11 KSP Residual norm 2.78381e-07 
+   12 KSP Residual norm 1.11244e-07 
+   13 KSP Residual norm 4.42854e-08 
+   14 KSP Residual norm 2.04564e-08 
+  5 SNES Function norm 3.33707e-08 
+    0 KSP Residual norm 1.66742e-07 
+    1 KSP Residual norm 7.62914e-08 
+    2 KSP Residual norm 3.18992e-08 
+    3 KSP Residual norm 1.33728e-08 
+    4 KSP Residual norm 5.28412e-09 
+    5 KSP Residual norm 2.70809e-09 
+    6 KSP Residual norm 1.68188e-09 
+    7 KSP Residual norm 9.450e-10 
+    8 KSP Residual norm 4.250e-10 
+    9 KSP Residual norm 1.778e-10 
+   10 KSP Residual norm 7.143e-11 
+   11 KSP Residual norm 4.171e-11 
+   12 KSP Residual norm 2.115e-11 
+   13 KSP Residual norm 1.118e-11 
+   14 KSP Residual norm < 1.e-11
+   15 KSP Residual norm < 1.e-11
+   16 KSP Residual norm < 1.e-11
+  6 SNES Function norm < 1.e-11
+Algebraic residual        |x|_1 6.18e-12  |x|_2 2.59e-13  |x|_inf 4.08e-14
+Interpolation residual    |x|_1 3.13e-02  |x|_2 1.57e-03  |x|_inf 2.55e-04
+Pointwise solution error  |x|_1 1.13e-03  |x|_2 7.50e-04  |x|_inf 2.66e-03
+Pointwise gradient error  |x|_1 4.85e+00  |x|_2 5.11e+00  |x|_inf 1.70e+01