snes/utils/convest.c

#include "petscsys.h"
#include <petscconvest.h> /*I "petscconvest.h" I*/
#include <petscdmplex.h>
#include <petscds.h>

#include <petsc/private/petscconvestimpl.h>

static PetscErrorCode zero_private(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
{
  PetscInt c;
  for (c = 0; c < Nc; ++c) u[c] = 0.0;
  return PETSC_SUCCESS;
}

/*@
  PetscConvEstDestroy - Destroys a PETSc convergence estimator `PetscConvEst` object

  Collective

  Input Parameter:
. ce - The `PetscConvEst` object

  Level: beginner

.seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
@*/
PetscErrorCode PetscConvEstDestroy(PetscConvEst *ce)
{
  PetscFunctionBegin;
  if (!*ce) PetscFunctionReturn(PETSC_SUCCESS);
  PetscValidHeaderSpecific(*ce, PETSC_OBJECT_CLASSID, 1);
  if (--((PetscObject)*ce)->refct > 0) {
    *ce = NULL;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(PetscFree3((*ce)->initGuess, (*ce)->exactSol, (*ce)->ctxs));
  PetscCall(PetscFree2((*ce)->dofs, (*ce)->errors));
  PetscCall(PetscHeaderDestroy(ce));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstSetFromOptions - Sets a convergence estimator `PetscConvEst` object based on values in the options database

  Collective

  Input Parameter:
. ce - The `PetscConvEst` object

  Level: beginner

.seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
@*/
PetscErrorCode PetscConvEstSetFromOptions(PetscConvEst ce)
{
  PetscFunctionBegin;
  PetscOptionsBegin(PetscObjectComm((PetscObject)ce), "", "Convergence Estimator Options", "PetscConvEst");
  PetscCall(PetscOptionsInt("-convest_num_refine", "The number of refinements for the convergence check", "PetscConvEst", ce->Nr, &ce->Nr, NULL));
  PetscCall(PetscOptionsReal("-convest_refine_factor", "The increase in resolution in each dimension", "PetscConvEst", ce->r, &ce->r, NULL));
  PetscCall(PetscOptionsBool("-convest_monitor", "Monitor the error for each convergence check", "PetscConvEst", ce->monitor, &ce->monitor, NULL));
  PetscCall(PetscOptionsBool("-convest_no_refine", "Debugging flag to run on the same mesh each time", "PetscConvEst", ce->noRefine, &ce->noRefine, NULL));
  PetscOptionsEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstView - Views a `PetscConvEst` object

  Collective

  Input Parameters:
+ ce     - The `PetscConvEst` object
- viewer - The `PetscViewer`

  Level: beginner

.seealso: `PetscConvEst`, `PetscViewer`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
@*/
PetscErrorCode PetscConvEstView(PetscConvEst ce, PetscViewer viewer)
{
  PetscFunctionBegin;
  PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)ce, viewer));
  PetscCall(PetscViewerASCIIPrintf(viewer, "ConvEst with %" PetscInt_FMT " levels\n", ce->Nr + 1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstGetSolver - Gets the solver used to produce discrete solutions

  Not Collective

  Input Parameter:
. ce - The `PetscConvEst` object

  Output Parameter:
. solver - The solver

  Level: intermediate

.seealso: `PetscConvEst`, `PetscConvEstSetSolver()`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
@*/
PetscErrorCode PetscConvEstGetSolver(PetscConvEst ce, PetscObject *solver)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ce, PETSC_OBJECT_CLASSID, 1);
  PetscAssertPointer(solver, 2);
  *solver = ce->solver;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstSetSolver - Sets the solver used to produce discrete solutions

  Not Collective

  Input Parameters:
+ ce     - The `PetscConvEst` object
- solver - The solver, must be a `KSP`, `SNES`, or `TS` object with an attached `DM`/`DS`, that can compute an exact solution

  Level: intermediate

.seealso: `PetscConvEst`, `PetscConvEstGetSNES()`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
@*/
PetscErrorCode PetscConvEstSetSolver(PetscConvEst ce, PetscObject solver)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ce, PETSC_OBJECT_CLASSID, 1);
  PetscValidHeader(solver, 2);
  ce->solver = solver;
  PetscUseTypeMethod(ce, setsolver, solver);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstSetUp - After the solver is specified, create data structures needed for estimating convergence

  Collective

  Input Parameter:
. ce - The `PetscConvEst` object

  Level: beginner

.seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
@*/
PetscErrorCode PetscConvEstSetUp(PetscConvEst ce)
{
  PetscInt Nf, f, Nds, s;

  PetscFunctionBegin;
  PetscCall(DMGetNumFields(ce->idm, &Nf));
  ce->Nf = PetscMax(Nf, 1);
  PetscCall(PetscMalloc2((ce->Nr + 1) * ce->Nf, &ce->dofs, (ce->Nr + 1) * ce->Nf, &ce->errors));
  PetscCall(PetscCalloc3(ce->Nf, &ce->initGuess, ce->Nf, &ce->exactSol, ce->Nf, &ce->ctxs));
  for (f = 0; f < Nf; ++f) ce->initGuess[f] = zero_private;
  PetscCall(DMGetNumDS(ce->idm, &Nds));
  for (s = 0; s < Nds; ++s) {
    PetscDS         ds;
    DMLabel         label;
    IS              fieldIS;
    const PetscInt *fields;
    PetscInt        dsNf;

    PetscCall(DMGetRegionNumDS(ce->idm, s, &label, &fieldIS, &ds, NULL));
    PetscCall(PetscDSGetNumFields(ds, &dsNf));
    if (fieldIS) PetscCall(ISGetIndices(fieldIS, &fields));
    for (f = 0; f < dsNf; ++f) {
      const PetscInt field = fields[f];
      PetscCall(PetscDSGetExactSolution(ds, field, &ce->exactSol[field], &ce->ctxs[field]));
    }
    if (fieldIS) PetscCall(ISRestoreIndices(fieldIS, &fields));
  }
  for (f = 0; f < Nf; ++f) PetscCheck(ce->exactSol[f], PetscObjectComm((PetscObject)ce), PETSC_ERR_ARG_WRONG, "DS must contain exact solution functions in order to estimate convergence, missing for field %" PetscInt_FMT, f);
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscConvEstComputeInitialGuess(PetscConvEst ce, PetscInt r, DM dm, Vec u)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ce, PETSC_OBJECT_CLASSID, 1);
  if (dm) PetscValidHeaderSpecific(dm, DM_CLASSID, 3);
  PetscValidHeaderSpecific(u, VEC_CLASSID, 4);
  PetscUseTypeMethod(ce, initguess, r, dm, u);
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscConvEstComputeError(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ce, PETSC_OBJECT_CLASSID, 1);
  if (dm) PetscValidHeaderSpecific(dm, DM_CLASSID, 3);
  PetscValidHeaderSpecific(u, VEC_CLASSID, 4);
  PetscAssertPointer(errors, 5);
  PetscUseTypeMethod(ce, computeerror, r, dm, u, errors);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstMonitorDefault - Monitors the convergence estimation loop

  Collective

  Input Parameters:
+ ce - The `PetscConvEst` object
- r  - The refinement level

  Options Database Key:
. -convest_monitor - Activate the monitor

  Level: intermediate

.seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`, `SNESSolve()`, `TSSolve()`
@*/
PetscErrorCode PetscConvEstMonitorDefault(PetscConvEst ce, PetscInt r)
{
  MPI_Comm comm;
  PetscInt f;

  PetscFunctionBegin;
  if (ce->monitor) {
    PetscInt  *dofs   = &ce->dofs[r * ce->Nf];
    PetscReal *errors = &ce->errors[r * ce->Nf];

    PetscCall(PetscObjectGetComm((PetscObject)ce, &comm));
    PetscCall(PetscPrintf(comm, "N: "));
    if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "["));
    for (f = 0; f < ce->Nf; ++f) {
      if (f > 0) PetscCall(PetscPrintf(comm, ", "));
      PetscCall(PetscPrintf(comm, "%7" PetscInt_FMT, dofs[f]));
    }
    if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "]"));
    PetscCall(PetscPrintf(comm, "  "));
    PetscCall(PetscPrintf(comm, "L_2 Error: "));
    if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "["));
    for (f = 0; f < ce->Nf; ++f) {
      if (f > 0) PetscCall(PetscPrintf(comm, ", "));
      if (errors[f] < 1.0e-11) PetscCall(PetscPrintf(comm, "< 1e-11"));
      else PetscCall(PetscPrintf(comm, "%g", (double)errors[f]));
    }
    if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "]"));
    PetscCall(PetscPrintf(comm, "\n"));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscConvEstSetSNES_Private(PetscConvEst ce, PetscObject solver)
{
  PetscClassId id;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetClassId(ce->solver, &id));
  PetscCheck(id == SNES_CLASSID, PetscObjectComm((PetscObject)ce), PETSC_ERR_ARG_WRONG, "Solver was not a SNES");
  PetscCall(SNESGetDM((SNES)ce->solver, &ce->idm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscConvEstInitGuessSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u)
{
  PetscFunctionBegin;
  PetscCall(DMProjectFunction(dm, 0.0, ce->initGuess, ce->ctxs, INSERT_VALUES, u));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscConvEstComputeErrorSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
{
  const char *prefix;
  PetscBool   errorView = PETSC_FALSE;

  PetscFunctionBegin;
  PetscCall(DMComputeL2FieldDiff(dm, 0.0, ce->exactSol, ce->ctxs, u, errors));
  PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ce, &prefix));
  PetscCall(PetscOptionsHasName(NULL, prefix, "-convest_error_view", &errorView));
  if (errorView) {
    DM                    dmError;
    PetscFE               feError, fe;
    PetscQuadrature       quad;
    Vec                   e;
    PetscDS               ds;
    PetscSimplePointFunc *funcs;
    void                **ctxs;
    PetscInt              dim, Nf;

    PetscCall(DMGetDimension(dm, &dim));
    PetscCall(DMGetDS(dm, &ds));
    PetscCall(PetscDSGetNumFields(ds, &Nf));
    PetscCall(PetscMalloc2(Nf, &funcs, Nf, &ctxs));
    for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscDSGetExactSolution(ds, f, &funcs[f], &ctxs[f]));
    PetscCall(DMClone(dm, &dmError));
    PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, 0, PETSC_DETERMINE, &feError));
    PetscCall(DMGetField(dm, 0, NULL, (PetscObject *)&fe));
    PetscCall(PetscFEGetQuadrature(fe, &quad));
    PetscCall(PetscFESetQuadrature(feError, quad));
    PetscCall(DMSetField(dmError, 0, NULL, (PetscObject)feError));
    PetscCall(PetscFEDestroy(&feError));
    PetscCall(DMCreateDS(dmError));
    PetscCall(DMGetGlobalVector(dmError, &e));
    PetscCall(PetscObjectSetName((PetscObject)e, "Error"));
    PetscCall(DMPlexComputeL2DiffVec(dm, 0., funcs, ctxs, u, e));
    PetscCall(VecViewFromOptions(e, NULL, "-convest_error_view"));
    PetscCall(DMRestoreGlobalVector(dmError, &e));
    PetscCall(DMDestroy(&dmError));
    PetscCall(PetscFree2(funcs, ctxs));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscConvEstSetJacobianNullSpace_Private(PetscConvEst ce, SNES snes)
{
  DM       dm;
  PetscInt f;

  PetscFunctionBegin;
  PetscCall(SNESGetDM(snes, &dm));
  for (f = 0; f < ce->Nf; ++f) {
    PetscErrorCode (*nspconstr)(DM, PetscInt, PetscInt, MatNullSpace *);

    PetscCall(DMGetNullSpaceConstructor(dm, f, &nspconstr));
    if (nspconstr) {
      MatNullSpace nullsp;
      Mat          J;

      PetscCall((*nspconstr)(dm, f, f, &nullsp));
      PetscCall(SNESSetUp(snes));
      PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL));
      PetscCall(MatSetNullSpace(J, nullsp));
      PetscCall(MatNullSpaceDestroy(&nullsp));
      break;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscConvEstGetConvRateSNES_Private(PetscConvEst ce, PetscReal alpha[])
{
  SNES        snes = (SNES)ce->solver;
  DM         *dm;
  PetscObject disc;
  PetscReal  *x, *y, slope, intercept;
  PetscInt    Nr = ce->Nr, r, f, dim, oldlevel, oldnlev;
  void       *ctx;

  PetscFunctionBegin;
  PetscCheck(ce->r == 2.0, PetscObjectComm((PetscObject)ce), PETSC_ERR_SUP, "Only refinement factor 2 is currently supported (not %g)", (double)ce->r);
  PetscCall(DMGetDimension(ce->idm, &dim));
  PetscCall(DMGetApplicationContext(ce->idm, &ctx));
  PetscCall(DMPlexSetRefinementUniform(ce->idm, PETSC_TRUE));
  PetscCall(DMGetRefineLevel(ce->idm, &oldlevel));
  PetscCall(PetscMalloc1(Nr + 1, &dm));
  /* Loop over meshes */
  dm[0] = ce->idm;
  for (r = 0; r <= Nr; ++r) {
    Vec           u;
    PetscLogStage stage;
    char          stageName[PETSC_MAX_PATH_LEN];
    const char   *dmname, *uname;

    PetscCall(PetscSNPrintf(stageName, PETSC_MAX_PATH_LEN - 1, "ConvEst Refinement Level %" PetscInt_FMT, r));
    PetscCall(PetscLogStageGetId(stageName, &stage));
    if (stage < 0) PetscCall(PetscLogStageRegister(stageName, &stage));
    PetscCall(PetscLogStagePush(stage));
    if (r > 0) {
      if (!ce->noRefine) {
        PetscCall(DMRefine(dm[r - 1], MPI_COMM_NULL, &dm[r]));
        PetscCall(DMSetCoarseDM(dm[r], dm[r - 1]));
      } else {
        DM cdm, rcdm;

        PetscCall(DMClone(dm[r - 1], &dm[r]));
        PetscCall(DMCopyDisc(dm[r - 1], dm[r]));
        PetscCall(DMGetCoordinateDM(dm[r - 1], &cdm));
        PetscCall(DMGetCoordinateDM(dm[r], &rcdm));
        PetscCall(DMCopyDisc(cdm, rcdm));
      }
      PetscCall(DMCopyTransform(ce->idm, dm[r]));
      PetscCall(PetscObjectGetName((PetscObject)dm[r - 1], &dmname));
      PetscCall(PetscObjectSetName((PetscObject)dm[r], dmname));
      for (f = 0; f < ce->Nf; ++f) {
        PetscErrorCode (*nspconstr)(DM, PetscInt, PetscInt, MatNullSpace *);

        PetscCall(DMGetNullSpaceConstructor(dm[r - 1], f, &nspconstr));
        PetscCall(DMSetNullSpaceConstructor(dm[r], f, nspconstr));
      }
    }
    PetscCall(DMViewFromOptions(dm[r], NULL, "-conv_dm_view"));
    /* Create solution */
    PetscCall(DMCreateGlobalVector(dm[r], &u));
    PetscCall(DMGetField(dm[r], 0, NULL, &disc));
    PetscCall(PetscObjectGetName(disc, &uname));
    PetscCall(PetscObjectSetName((PetscObject)u, uname));
    /* Setup solver */
    PetscCall(SNESReset(snes));
    PetscCall(SNESSetDM(snes, dm[r]));
    PetscCall(DMPlexSetSNESLocalFEM(dm[r], PETSC_FALSE, ctx));
    PetscCall(DMPlexSetSNESVariableBounds(dm[r], snes));
    PetscCall(SNESSetFromOptions(snes));
    /* Set nullspace for Jacobian */
    PetscCall(PetscConvEstSetJacobianNullSpace_Private(ce, snes));
    /* Create initial guess */
    PetscCall(PetscConvEstComputeInitialGuess(ce, r, dm[r], u));
    PetscCall(SNESSolve(snes, NULL, u));
    PetscCall(PetscLogEventBegin(ce->event, ce, 0, 0, 0));
    PetscCall(PetscConvEstComputeError(ce, r, dm[r], u, &ce->errors[r * ce->Nf]));
    PetscCall(PetscLogEventEnd(ce->event, ce, 0, 0, 0));
    for (f = 0; f < ce->Nf; ++f) {
      PetscSection s, fs;
      PetscInt     lsize;

      /* Could use DMGetOutputDM() to add in Dirichlet dofs */
      PetscCall(DMGetLocalSection(dm[r], &s));
      PetscCall(PetscSectionGetField(s, f, &fs));
      PetscCall(PetscSectionGetConstrainedStorageSize(fs, &lsize));
      PetscCallMPI(MPIU_Allreduce(&lsize, &ce->dofs[r * ce->Nf + f], 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)snes)));
      PetscCall(PetscLogEventSetDof(ce->event, f, ce->dofs[r * ce->Nf + f]));
      PetscCall(PetscLogEventSetError(ce->event, f, ce->errors[r * ce->Nf + f]));
    }
    /* Monitor */
    PetscCall(PetscConvEstMonitorDefault(ce, r));
    if (!r) {
      /* PCReset() does not wipe out the level structure */
      KSP ksp;
      PC  pc;

      PetscCall(SNESGetKSP(snes, &ksp));
      PetscCall(KSPGetPC(ksp, &pc));
      PetscCall(PCMGGetLevels(pc, &oldnlev));
    }
    /* Cleanup */
    PetscCall(VecDestroy(&u));
    PetscCall(PetscLogStagePop());
  }
  for (r = 1; r <= Nr; ++r) PetscCall(DMDestroy(&dm[r]));
  /* Fit convergence rate */
  PetscCall(PetscMalloc2(Nr + 1, &x, Nr + 1, &y));
  for (f = 0; f < ce->Nf; ++f) {
    for (r = 0; r <= Nr; ++r) {
      x[r] = PetscLog10Real(ce->dofs[r * ce->Nf + f]);
      y[r] = PetscLog10Real(ce->errors[r * ce->Nf + f]);
    }
    PetscCall(PetscLinearRegression(Nr + 1, x, y, &slope, &intercept));
    /* Since h^{-dim} = N, lg err = s lg N + b = -s dim lg h + b */
    alpha[f] = -slope * dim;
  }
  PetscCall(PetscFree2(x, y));
  PetscCall(PetscFree(dm));
  /* Restore solver */
  PetscCall(SNESReset(snes));
  {
    /* PCReset() does not wipe out the level structure */
    KSP ksp;
    PC  pc;

    PetscCall(SNESGetKSP(snes, &ksp));
    PetscCall(KSPGetPC(ksp, &pc));
    PetscCall(PCMGSetLevels(pc, oldnlev, NULL));
    PetscCall(DMSetRefineLevel(ce->idm, oldlevel)); /* The damn DMCoarsen() calls in PCMG can reset this */
  }
  PetscCall(SNESSetDM(snes, ce->idm));
  PetscCall(DMPlexSetSNESLocalFEM(ce->idm, PETSC_FALSE, ctx));
  PetscCall(DMPlexSetSNESVariableBounds(ce->idm, snes));
  PetscCall(SNESSetFromOptions(snes));
  PetscCall(PetscConvEstSetJacobianNullSpace_Private(ce, snes));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstGetConvRate - Returns an estimate of the convergence rate for the discretization

  Not Collective

  Input Parameter:
. ce - The `PetscConvEst` object

  Output Parameter:
. alpha - The convergence rate for each field

  Options Database Keys:
+ -snes_convergence_estimate - Execute convergence estimation inside `SNESSolve()` and print out the rate
- -ts_convergence_estimate   - Execute convergence estimation inside `TSSolve()` and print out the rate

  Level: intermediate

  Notes:
  The convergence rate alpha is defined by
$ || u_\Delta - u_exact || < C \Delta^alpha
  where u_\Delta is the discrete solution, and Delta is a measure of the discretization size. We usually use h for the
  spatial resolution and \Delta t for the temporal resolution.

  We solve a series of problems using increasing resolution (refined meshes or decreased timesteps), calculate an error
  based upon the exact solution in the `PetscDS`, and then fit the result to our model above using linear regression.

.seealso: `PetscConvEstSetSolver()`, `PetscConvEstCreate()`, `SNESSolve()`, `TSSolve()`
@*/
PetscErrorCode PetscConvEstGetConvRate(PetscConvEst ce, PetscReal alpha[])
{
  PetscInt f;

  PetscFunctionBegin;
  if (ce->event < 0) PetscCall(PetscLogEventRegister("ConvEst Error", PETSC_OBJECT_CLASSID, &ce->event));
  for (f = 0; f < ce->Nf; ++f) alpha[f] = 0.0;
  PetscUseTypeMethod(ce, getconvrate, alpha);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstRateView - Displays the convergence rate obtained from `PetscConvEstGetConvRate()` using a `PetscViewer`

  Collective

  Input Parameters:
+ ce     - iterative context obtained from `SNESCreate()`
. alpha  - the convergence rate for each field
- viewer - the viewer to display the reason

  Options Database Key:
. -snes_convergence_estimate - print the convergence rate

  Level: developer

.seealso: `PetscConvEst`, `PetscConvEstGetConvRate()`
@*/
PetscErrorCode PetscConvEstRateView(PetscConvEst ce, const PetscReal alpha[], PetscViewer viewer)
{
  PetscBool isAscii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isAscii));
  if (isAscii) {
    PetscInt Nf = ce->Nf, f;

    PetscCall(PetscViewerASCIIAddTab(viewer, ((PetscObject)ce)->tablevel));
    PetscCall(PetscViewerASCIIPrintf(viewer, "L_2 convergence rate: "));
    if (Nf > 1) PetscCall(PetscViewerASCIIPrintf(viewer, "["));
    for (f = 0; f < Nf; ++f) {
      if (f > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
      PetscCall(PetscViewerASCIIPrintf(viewer, "%#.2g", (double)alpha[f]));
    }
    if (Nf > 1) PetscCall(PetscViewerASCIIPrintf(viewer, "]"));
    PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
    PetscCall(PetscViewerASCIISubtractTab(viewer, ((PetscObject)ce)->tablevel));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscConvEstCreate - Create a `PetscConvEst` object. This is used to study the convergence rate of approximations on grids to a continuum solution

  Collective

  Input Parameter:
. comm - The communicator for the `PetscConvEst` object

  Output Parameter:
. ce - The `PetscConvEst` object

  Level: beginner

.seealso: `PetscConvEst`, `PetscConvEstDestroy()`, `PetscConvEstGetConvRate()`, `DMAdaptorCreate()`, `DMAdaptor`
@*/
PetscErrorCode PetscConvEstCreate(MPI_Comm comm, PetscConvEst *ce)
{
  PetscFunctionBegin;
  PetscAssertPointer(ce, 2);
  PetscCall(PetscSysInitializePackage());
  PetscCall(PetscHeaderCreate(*ce, PETSC_OBJECT_CLASSID, "PetscConvEst", "ConvergenceEstimator", "SNES", comm, PetscConvEstDestroy, PetscConvEstView));
  (*ce)->monitor           = PETSC_FALSE;
  (*ce)->r                 = 2.0;
  (*ce)->Nr                = 4;
  (*ce)->event             = -1;
  (*ce)->ops->setsolver    = PetscConvEstSetSNES_Private;
  (*ce)->ops->initguess    = PetscConvEstInitGuessSNES_Private;
  (*ce)->ops->computeerror = PetscConvEstComputeErrorSNES_Private;
  (*ce)->ops->getconvrate  = PetscConvEstGetConvRateSNES_Private;
  PetscFunctionReturn(PETSC_SUCCESS);
}